<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                             ----------------------

                                    FORM 10-Q

                  QUARTERLY REPORT UNDER SECTION 13 OR 15(D) OF
                       THE SECURITIES EXCHANGE ACT OF 1934

                     For the quarter ended December 31, 1998

                        Commission file number 001-13950



                           CENTRAL PARKING CORPORATION
--------------------------------------------------------------------------------
             (Exact Name of Registrant as Specified in Its Charter)



<TABLE>
<S>                                                                    <C>
                   Tennessee                                                        62-1052916
 ---------------------------------------------                         ------------------------------------
 (State or Other Jurisdiction of Incorporation                         (I.R.S. Employer Identification No.)
               or Organization)


             2401 21st Avenue South,
         Suite 200, Nashville, Tennessee                                               37212
 ---------------------------------------------                         ------------------------------------
    (Address of Principal Executive Offices)                                        (Zip Code)


Registrant's Telephone Number, Including Area Code:                            (615) 297-4255
                                                                       ------------------------------------


Former name, address and fiscal year, if changed since last report:               Not Applicable
                                                                       ------------------------------------
</TABLE>


Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. YES X NO ___


Indicate the number of shares outstanding of each of the registrant's classes of
common stock as of the latest practicable date.


<TABLE>
<CAPTION>
                Class                                                     Outstanding at February 11, 1999
 ---------------------------------------------                         ------------------------------------
<S>                                                                       <C>
       Common Stock, $0.01 par value                                                29,583,005
</TABLE>



<PAGE>   2




                                      INDEX

                           CENTRAL PARKING CORPORATION


<TABLE>
<CAPTION>
PART 1.       FINANCIAL INFORMATION                                                                                PAGE
-------       ---------------------                                                                                ----
<S>           <C>                                                                                                 <C>
Item 1.       Financial Statements (Unaudited)

              Condensed consolidated balance sheets
              --- December 31, 1998, September 30, 1998, and December 31, 1997..............................          3

              Condensed consolidated statements of earnings
              --- three months ended December 31, 1998 and 1997.............................................          4

              Condensed consolidated statements of cash flows
              --- three months ended December 31, 1998 and 1997.............................................          5

              Notes to condensed consolidated financial statements..........................................      6 - 9

Item 2.       Management's Discussion and Analysis of Financial
              Condition and Results of Operations...........................................................    10 - 14


PART 2.       OTHER INFORMATION
-------       -----------------

Item 4.       Submission of Matters to a Vote of Security Holders...........................................         15

Item 6.       Exhibits and Reports on Form 8-K..............................................................         15


              SIGNATURES ...................................................................................         16
              ----------
</TABLE>


<PAGE>   3
                                     PART 1

                          Item 1. Financial Statements

                  CENTRAL PARKING CORPORATION AND SUBSIDIARIES
                      CONDENSED CONSOLIDATED BALANCE SHEETS

Dollar amounts in thousands

<TABLE>
<CAPTION>
                                                                                    UNAUDITED                       UNAUDITED
                                                                                   DECEMBER 31,    SEPTEMBER 30,   DECEMBER 31,
                                ASSETS                                                1998             1998           1997
                                ------                                                -----            -----          ----
<S>                                                                                <C>             <C>             <C>
Current assets:
     Cash and cash equivalents                                                     $  20,000       $  19,840       $  13,288
     Management accounts receivable                                                   23,202          17,387          11,164
     Accounts and current portion of notes receivable - other                         19,779          11,347           4,790
     Prepaid expenses                                                                 22,166          18,167          11,314
     Deferred income taxes                                                               545             545             981
     Prepaid and refundable income taxes                                               1,266           1,266              --
                                                                                   ---------       ---------       ---------

           Total current assets                                                       86,958          68,552          41,537



Investments, at amortized cost                                                         5,152           5,087           4,825
Notes receivable, less current portion                                                22,718          25,110          11,208
Property, equipment, and leasehold improvements, net                                 121,363         118,176          80,177
Contract and lease rights, net                                                        17,359          17,773           4,807
Goodwill, net                                                                        252,829         254,997          51,584
Investment in and advances to partnerships and joint ventures                         37,185          37,344          56,125
Other assets                                                                          21,469          17,834           6,481
                                                                                   ---------       ---------       ---------

                                                                                   $ 565,033       $ 544,873       $ 256,744
                                                                                   =========       =========       =========

                 LIABILITIES AND SHAREHOLDERS' EQUITY

Current liabilities:
     Current portion of long-term debt and capital lease obligations               $   2,310       $   2,225       $   1,292
     Accounts payable                                                                 51,606          51,638          26,586
     Accrued payroll and related costs                                                 8,328          10,351           7,262
     Accrued expenses                                                                  9,474          10,102             751
     Management accounts payable                                                      20,879          17,415           9,928
     Income taxes payable                                                              5,611             945           3,690
                                                                                   ---------       ---------       ---------
           Total current liabilities                                                  98,208          92,676          49,509

Long-term debt and capital lease obligations                                          66,245          60,704          86,899
Deferred rent                                                                         12,755          12,938           4,029
Deferred compensation                                                                  4,484           3,797           3,118
Deferred income taxes                                                                  2,162           2,162           5,693
Other liabilities                                                                      6,679           6,892           5,293
                                                                                   ---------       ---------       ---------
           Total liabilities                                                         190,533         179,169         154,541

Company-obligated mandatorily redeemable convertible securities of subsidiary
     whose sole assets are convertible subordinated debentures
     of the Parent                                                                   110,000         110,000              --

Shareholders' equity:
     Common stock, $.01 par value; 50,000,000 shares authorized,
         29,579,630, 29,569,767, and 26,316,054
         issued and outstanding, respectively                                            296             296             263
     Additional paid-in capital                                                      166,933         166,740          33,050
     Foreign currency translation adjustment                                             527             359             271
     Retained earnings                                                                97,232          88,811          69,172
     Deferred compensation on restricted stock                                          (488)           (502)           (553)
                                                                                   ---------       ---------       ---------
           Total shareholders' equity                                                264,500         255,704         102,203
                                                                                   ---------       ---------       ---------
                                                                                   $ 565,033       $ 544,873       $ 256,744
                                                                                   =========       =========       =========
</TABLE>


     See accompanying notes to condensed consolidated financial statements



                                  Page 3 of 16
<PAGE>   4

                  CENTRAL PARKING CORPORATION AND SUBSIDIARIES
                  CONDENSED CONSOLIDATED STATEMENTS OF EARNINGS
                                    UNAUDITED

Dollar amounts in thousands, except per share data

<TABLE>
<CAPTION>
                                                                     THREE MONTHS ENDED DECEMBER 31,
                                                                           1998           1997
                                                                        ---------       --------
<S>                                                                     <C>             <C>     
Revenues:
      Parking                                                           $  99,644       $ 59,005
      Management contract                                                  15,148         11,264
                                                                        ---------       --------
               Total revenues                                             114,792         70,269

Costs and expenses:
      Cost of parking                                                      81,744         50,975
      Cost of management contracts                                          4,625          3,252
      General and administrative                                           10,340          6,641
      Goodwill and non-compete amortization                                 2,595            597
                                                                        ---------       --------
               Total costs and expenses                                    99,304         61,465
                                                                        ---------       --------

               Operating earnings                                          15,488          8,804

Other income (expenses):
      Interest income                                                         826            497
      Interest expense                                                     (1,232)        (1,411)
      Dividends on company-obligated mandatorily
           redeemable convertible securities of a subsidiary trust         (1,396)            --
      Net gains on sales of property and equipment                              1              2
      Equity in partnership and joint venture earnings                      1,087          1,207
                                                                        ---------       --------
               Other income (expenses), net                                  (714)           295
                                                                        ---------       --------

               Earnings before income taxes                                14,774          9,099

               Income taxes                                                 5,910          3,457
                                                                        ---------       --------

               Net earnings                                             $   8,864       $  5,642
                                                                        =========       ========

Basic weighted average common shares
      outstanding                                                          29,310         26,042
                                                                        =========       ========

Basic earnings per common share                                         $    0.30       $   0.22
                                                                        =========       ========

Diluted weighted average common shares and
      dilutive potential common shares                                     29,717         26,482
                                                                        =========       ========

Diluted earnings per common share                                       $    0.30       $   0.21
                                                                        =========       ========
</TABLE>


See accompanying notes to condensed consolidated financial statements



                                  Page 4 of 16
<PAGE>   5

                  CENTRAL PARKING CORPORATION AND SUBSIDIARIES
                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                                    UNAUDITED

Dollar amounts in thousands

<TABLE>
<CAPTION>
                                                                                         THREE MONTHS ENDED DECEMBER 31,
                                                                                               1998           1997
                                                                                               ----           ----
<S>                                                                                        <C>            <C>
Cash flows from operating activities:
  Net earnings                                                                             $  8,864       $  5,642
  Adjustments to reconcile net earnings to net cash provided by operating activities:
     Depreciation                                                                             1,622          1,054
     Amortization of goodwill and non-compete agreements                                      2,595            597
     Amortization of contract and lease rights, straight-line rent,
        deferred financing fees and other                                                       789            266
     Equity in partnership and joint venture (earnings)                                      (1,087)        (1,207)
     Distributions from partnerships and joint ventures                                       1,246          1,313
     Net gains on sales of property and equipment                                                (1)            (2)
     Deferred income taxes                                                                       --            247
     Changes in operating assets and liabilities, excluding effects of
        acquisitions:
        (Increase) decrease in management accounts receivable                                (5,815)          (157)
        (Increase) decrease in notes and accounts receivable - other                         (5,982)         2,191
        (Increase) decrease in prepaid expenses                                              (3,999)        (1,573)
        (Increase) decrease in prepaid and refundable income taxes                               --          2,154
        (Increase) decrease in other assets                                                  (3,835)          (103)
        Increase (decrease) in accounts payable, accrued expenses
             other liabilities and deferred compensation                                     (2,528)          (442)
        Increase (decrease) in management accounts payable                                    3,464         (1,321)
        Increase (decrease) in income taxes payable                                           4,666          2,577
                                                                                           --------       --------
     Net cash provided (used) by operating activities                                            (1)        11,236
                                                                                           --------       --------

Cash flows from investing activities:
  Proceeds from sales of property and equipment                                                  21             62
  Investments in notes receivable                                                               (58)            (3)
  Purchase of property, equipment, and leasehold improvements                                (4,829)        (2,063)
  Investment in and advances to partnerships and joint ventures
     and unconsolidated subsidiaries                                                             --             75
  Acquisitions of companies net of cash acquired                                                 --        (12,258)
  Purchase of investments                                                                       (65)           (71)
                                                                                           --------       --------
     Net cash used by investing activities                                                   (4,931)       (14,258)
                                                                                           --------       --------

Cash flows from financing activities:
  Dividends paid                                                                               (444)          (395)
  Net borrowings (repayments) under revolving credit agreement, net of issuance costs         5,800          6,550
  Principal repayments on notes payable                                                        (625)          (109)
  Distribution from partnerships and joint ventures                                              --
  Proceeds from issuance of common stock and exercise of stock options, net                     193            207
                                                                                           --------       --------
     Net cash provided by financing activities                                                4,924          6,253
                                                                                           --------       --------

Foreign currency translation                                                                    168             78
                                                                                           --------       --------
     Net increase (decrease)  in cash and cash equivalents                                      160          3,309
Cash and cash equivalents at beginning of period                                             19,840          9,979
                                                                                           --------       --------

Cash and cash equivalents at end of period                                                 $ 20,000       $ 13,288
                                                                                           ========       ========

Non-cash transactions:
  Issuance of restricted stock                                                             $     24       $     --
                                                                                           ========       ========

Effects of acquisitions:
     Fair value of assets acquired                                                         $     --       $  4,246
     Purchase price in excess of the net assets acquired                                         --         20,258
     Estimated fair value of liabilities assumed in acquisitions                                 --        (11,064)
                                                                                           --------       --------
     Cash paid                                                                                   --         13,440
     Less cash acquired                                                                          --         (1,182)
                                                                                           --------       --------
     Net cash paid for acquisition                                                         $     --       $ 12,258
                                                                                           ========       ========
</TABLE>


See accompanying notes to condensed consolidated financial statements


                                  Page 5 of 16
<PAGE>   6


                           CENTRAL PARKING CORPORATION

        NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)


Basis of Presentation

The accompanying unaudited condensed consolidated financial statements have been
prepared in accordance with generally accepted accounting principles and with
the instructions to Form 10-Q and Article 10 of Regulation S-X. Accordingly,
they do not include all of the information and footnotes required by generally
accepted accounting principles for complete financial statements. In the opinion
of management, all adjustments (consisting of normal recurring accruals)
considered necessary for a fair presentation have been included. All significant
intercompany transactions have been eliminated in consolidation. Operating
results for the three months ended December 31, 1998 are not necessarily
indicative of the results that may be expected for the fiscal year ending
September 30, 1999. For further information, refer to the consolidated financial
statements and footnotes thereto for the year ended September 30, 1998 (included
in the Company's Annual Report on Form 10-K). Certain items have been restated
to conform to current year presentation.

Stock Split

On November 21, 1997, the Board of Directors approved a three-for-two stock
split payable to shareholders of record as of December 5, 1997. The stock split
was distributed on December 12, 1997, resulting in the net issuance of 8,771,363
new shares. All shares and per share amounts in this report have been adjusted
to reflect the stock split.

Earnings Per Share

Basic earnings per share excludes dilution and is computed by dividing income
available to common shareholders by the weighted-average number of common shares
outstanding for the period. Diluted earnings per share reflects the potential
dilution that could occur if securities or other contracts to issue common stock
were exercised or converted into common stock or resulted in the issuance of
common stock that then shared in the earnings of the entity. Earnings per share
for all periods presented have been calculated and presented in accordance with
SFAS No. 128.

The following tables set forth the computation of basic and diluted earnings per
share:

<TABLE>
<CAPTION>
                                                           Three Months Ended                      Three Months Ended
                                                            December 31, 1998                       December 31, 1997
                                                    Income        Common       Per-Share      Income    Common     Per-Share
                                                  Available       Shares        Amount      Available   Shares      Amount
                                                   ($000's)       (000's)                    ($000's)   (000's)

<S>                                               <C>             <C>          <C>          <C>         <C>        <C>
Basic earnings per share                            $8,864         29,310       $0.30        $5,642     26,042        $0.22

Effect of dilutive stock and options:
   Stock option plan                                                  173                                  233        (0.01)
   Restricted stock plan                                              172                                  166
   Deferred stock unit plan                                            16                                    -
   Employee stock purchase plan                                        46                                   41

Diluted earnings per share                          $8,864         29,717       $0.30        $5,642     26,482        $0.21
</TABLE>



                                  Page 6 of 16
<PAGE>   7


Weighted average common shares used for the computation of basic earnings per
share excludes certain common shares issued pursuant to the Company's restricted
stock plan because under the related deferred compensation agreement the officer
forfeits such shares if he voluntarily terminates his employment with the
Company. The effect of the conversion of the company-obligated mandatorily
redeemable securities of the subsidiary trust has not been included in the
diluted earnings per share calculation since such securities are anti-dilutive.
At December 31, 1998, such securities were convertible into 2,000,000 shares of
common stock.

Long Term Debt

On February 11, 1998, the Company established a new credit facility (the "Credit
Facility") providing for an aggregate availability of up to $300 million,
consisting of a five-year $200 million revolving credit facility, including a
sub-limit of $25 million for standby letters of credit, and a $100 million term
loan. The Credit Facility bore interest until June 30, 1998 at a rate of LIBOR
plus 1.25%. On June 30, 1998 the interest rate on the Credit Facility and the
commitment fee on the unused portion reverted to a grid pricing based upon the
achievement of various financial ratios. The Credit Facility contains certain
covenants including those that require the Company to maintain certain financial
ratios, restrict further indebtedness, and limit the amount of dividends
payable. On March 18, 1998, the Company completed offerings of equity and
convertible trust issued preferred securities, from which the Company obtained
$195.6 million in net proceeds. The Company repaid and terminated the $100
million term loan with proceeds from these offerings. The remaining $95.6
million in proceeds was applied to reduce the outstanding balance under the $200
million revolving credit facility. The amount outstanding under the Company's
Credit Facility as of December 31, 1998 is $54.0 million, with a weighted
average interest rate of 6.24% for the quarter ended December 31, 1998.

    In February 1999, Central Parking obtained a commitment, which expires March
31, 1999, to establish a new credit facility providing for an aggregate of up to
$400 million (the "New Credit Commitment") consisting of a five-year $200
million revolving credit facility including a sublimit of $25 million for
standby letters of credit, and a $200 million five-year term loan with scheduled
repayment consisting of $50 million per year, beginning in year two. The New
Credit Commitment will bear interest at either prime rate plus 0.5% or LIBOR
plus a margin of 1.12% and after three months revert to a grid pricing at a
margin of 0.25% to 1.25% based upon Central Parking achieving a number of
financial ratios. The New Credit Commitment will contain certain covenants
including those that require Central Parking to maintain certain financial
ratios, restrict further indebtedness and limit the amount of dividends paid.
Central Parking intends to use the New Credit Commitment to replace Central
Parking's Credit Facility and to refinance the existing debt of Allright
Holdings, Inc. (see subsequent note - Pending Merger)

Convertible Trust Issued Preferred Securities and Equity Offerings

On March 18, 1998, the Company created Central Parking Finance Trust ("Trust")
which completed a private placement of 4,400,000 shares at $25.00 per share of
5.25% convertible trust issued preferred securities ("Preferred Securities")
pursuant to an exemption from registration under the Securities Act of 1933, as
amended. The Preferred Securities represent preferred undivided beneficial
interests in the assets of Central Parking Finance Trust, a statutory business
trust formed under the laws of the State of Delaware. The Company owns all of
the common securities of the Trust. The Trust exists for the sole purpose of
issuing the Preferred Securities and investing the proceeds thereof in an
equivalent amount of 5.25% Convertible Subordinated Debentures ("Convertible
Debentures") of the Company due 2028. The net proceeds to the Company from the
Preferred Securities private placement were $106.5 million. Each Preferred
Security is entitled to receive cumulative cash distributions at an annual rate
of 5.25% (or $1.312 per share) and will be convertible at the option of the
holder thereof into shares of Company common stock at a conversion rate of
0.4545 shares of Company common stock for each Preferred Security (equivalent to
$55.00 per share of Company common stock), subject to adjustment in certain
circumstances. The Preferred Securities do not have a stated maturity date but
are subject to mandatory redemption upon the repayment of the Convertible
Debentures at their stated maturity (April 1, 2028) or upon acceleration or
earlier repayment of the Convertible Debentures.

The Company's consolidated balance sheets reflect the Preferred Securities of
the Trust as company-obligated mandatorily redeemable convertible securities of
subsidiary whose sole assets are convertible subordinated debentures of the
Parent.

Comprehensive Income

    In June 1997, the Financial Accounting Standards Board issued SFAS No. 130,
"Reporting Comprehensive Income" ("Statement 130"). Statement 130 established
standards for reporting and display of comprehensive income and its components.
Comprehensive income is the change in equity of a business enterprise during a
period from transactions



                                  Page 7 of 16
<PAGE>   8


and other events and circumstances from non-owner sources. Comprehensive income
includes all changes in equity except those resulting from investments by and
distributions to owners. The Company's other comprehensive income consists of
foreign currency translation, which is recorded to shareholders' equity, net of
tax. The foreign currency translation adjustments recorded for the three month
periods ended December 31, 1998 and 1997 were $168 thousand and $78 thousand,
respectively.

Proforma Information
The following unaudited pro forma condensed results of operations give effect to
the acquisition of Kinney System Holding Corp, ("Kinney"), Central Parking
System of Louisiana, Inc. ("CPS-Louisiana"), and Turner System Parking , Inc.
("Turner") as if such transactions had occurred at the beginning of each period
presented (in thousands except for earnings per share):
<TABLE>
<CAPTION>
                                                                                          Three Months Ended
                                                                                             December 31,
                                                                                                1997
                                                                                                ----
     <S>                                                                                  <C>
     Total revenues                                                                          $106,547
     Earnings before income taxes                                                               6,785
     Net earnings                                                                               3,462
     Basic earnings per share                                                                $   0.13
     Basic weighted average common shares outstanding                                          26,994
     Diluted earnings per share                                                              $   0.13
     Diluted weighted average common shares outstanding                                        27,434
</TABLE>

The foregoing unaudited proforma amounts are based upon certain assumptions and
estimates, including, but not limited to, the recognition of interest expense on
debt incurred to finance the acquisitions and amortization of goodwill over 5 to
30 years. The unaudited proforma amounts do not necessarily represent results
which would have occurred if the acquisitions had taken place on the basis
assumed above, nor are they indicative of the results of future combined
operations.

Year 2000 
    Central Parking has considered the impact of Year 2000 issues on its
computer systems and applications and has developed remediation plans. These
plans are part of Central Parking's ongoing business strategies to incorporate
advanced technologies in its information systems, and were contemplated in
advance of Year 2000 issues. The expenditures for system upgrades will be
accounted for as regular capital expenditures and will be depreciated over their
estimated useful lives of 3 - 5 years. The ongoing expenses of training and
testing will be expensed as they are incurred. It is estimated that Central
Parking will spend in excess of $2 million upgrading its computer information
systems in accordance with its plans for technological enhancement, and that
such expenditures will not be material to Central Parking's operations or
liquidity. Central Parking believes that the upgraded information systems will
be Year 2000 compliant. System hardware and software that in management's
estimation are not Year 2000 compliant have been fully depreciated. Central
Parking estimates that its information systems will be Year 2000 compliant by
April 1999. This should allow Central Parking adequate time to continue to test
and determine the compliance of such systems. Management believes that this is
enough time to fully test and foresee all significant remaining Year 2000 issues
on its information systems and, therefore, does not have any other contingency
plan in place for its information systems.

    Central Parking uses some fee calculation devices that compute parking fees
and statistical data, and also automate the ingress and egress control
mechanisms at certain parking facilities. Central Parking believes that less
than 20% of its operations have fee calculation devices with any Year 2000
issues with regard to carrying out its parking business. However, the vendors
have given no assurance that such fee computation devices will be Year 2000
compliant on any given date before December 31, 1999. In the event remediation
is not complete at any of these sites prior to the Year 2000, and a failure of
such equipment were to occur due to processing incompatibilities in the Year
2000, manual override systems are in place at all locations. Given the limited
technology required to operate such facilities, management believes all material
operations could adequately be performed manually. Such contingency plans are
currently deployed in the events of power failures or other business
interruptions at locations where these devices are located.

    Central Parking is communicating, by means of Year 2000 questionnaires, with
each of its major vendors to determine third party compliance with Year 2000
issues. Although Central Parking cannot require its vendors to respond,
follow-up with each party is being conducted to try and determine and resolve
any Year 2000 issues. Central



                                  Page 8 of 16
<PAGE>   9


Parking is also requiring all vendors to warrant that all software and hardware
purchased by Central Parking is fully Year 2000 compliant. While Central Parking
does not expect to be materially affected by any third party's Year 2000 issues,
no assurance can be given that a third party's failure to adequately address
their Year 2000 issues could not materially effect Central Parking's business or
financial results.

Pending Merger and Subsequent Events

         On September 21, 1998, the Company entered into a definitive agreement
pursuant to which the Company has agreed to merge with Allright Holdings, Inc.
("Allright"). Allright (d/b/a Allright Parking) is headquartered in Houston and
is one of the largest parking services companies in the United States with
revenues of $217.4 million for the fiscal year ended June 30, 1998. The
transaction, which is expected to be accounted for as a pooling-of-interests, is
valued using a base purchase price of $564.4 million. The base purchase price of
Allright will be adjusted for certain items such as assumed long-term
indebtedness, certain expenses, asset acquisitions or dispositions, and material
variations of amounts estimated or represented by Allright Management prior to
the closing date. The equity purchase price of Allright is calculated in
equivalent shares of Central Parking common stock, based on a fixed share price
of $46.00 per share. Under terms of the agreement, Central Parking expects to
issue approximately 7.6 million shares of common stock to the shareholders of
Allright. As of December 31, 1998, $1.0 million in merger-related expenses was
included in prepaid expenses on the accompanying consolidated balance sheet.
Upon consummation or termination of the merger, such amounts and other merger
related costs will be reflected as expenses in the statement of earnings. Upon
consummation of the merger, the Company estimates that total nonrecurring
charges directly attributable to the Merger for both companies combined will be
approximately $25.8 million.

    The merger remains subject to certain closing conditions, including the
expiration of the waiting period under the Hart-Scott-Rodino Act. The
transaction is subject to approval by the shareholders of both Central Parking
and Allright at separate meetings scheduled for February 17, 1999.

         On January 27, 1999, the Company entered into a conditional agreement
to purchase a parking facility, yet to be constructed, for approximately $34
million, subject to adjustment. The Company anticipates the facility will be
completed during the latter part of the year 2000. When completed, the parking
facility will have approximately 960 spaces. The Company anticipates funding the
commitment through its credit facility. Upon execution of the agreement, the
Company is required to provide an unconditional irrevocable guaranty of payment
to the seller.

         On February 12, 1999, Central Parking obtained a commitment, which
expires March 31, 1999, to establish a new credit facility providing for an
aggregate of up to $400 million (the "New Credit Commitment") consisting of a
five-year $200 million revolving credit facility including a sublimit of $25
million for standby letters of credit, and a $200 million five-year term loan
with scheduled repayment consisting of $50 million per year, beginning in year
two. The New Credit Commitment will bear interest at either prime rate plus 0.5%
or LIBOR plus a margin of 1.12% and after three months revert to a grid pricing
at a margin of 0.25% to 1.25% based upon Central Parking achieving a number of
financial ratios. The New Credit Commitment will contain certain covenants
including those that require Central Parking to maintain certain financial
ratios, restrict further indebtedness and limit the amount of dividends paid.
Central Parking intends to use the New Credit Commitment to replace the
Company's Credit Facility and to refinance the existing debt of Allright. The
Company's indebtedness will increase from approximately $68.6 million, as of
December 31, 1998, to approximately $333.6 million.



                                  Page 9 of 16
<PAGE>   10



Item 2.  Management's Discussion and Analysis of Financial Condition and Results
         of Operations

Special Cautionary Notice Regarding Forward-Looking Statements

         This Quarterly Report includes various forward-looking statements that
are subject to risks and uncertainties. Forward-looking statements include
discussions concerning future results of operations of the Company including,
without limitation, statements preceded by, followed by or that otherwise
include the words "believes," "expects," "anticipates," "intends," "estimates"
or similar expressions. For those statements, Central Parking claims the
protection of the safe harbor for forward-looking statements contained in the
Private Securities Litigation Reform Act of 1995.

         The following important factors, in addition to those discussed
elsewhere in this Quarterly Report, could affect the future financial results of
the Company and could cause actual results to differ materially from those
expressed in forward-looking statements contained in this document:

         -        successfully integrating Allright and Kinney Systems, as well
                  as past and future acquisitions in light of challenges in
                  retaining key employees, synchronizing business processes and
                  efficiently integrating facilities, marketing, and operations;

         -        successful implementation of the Company's operating and
                  growth strategy, including possible strategic acquisitions;

         -        fluctuations in quarterly operating results caused by a
                  variety of factors including the timing of gains on sales of
                  owned facilities, preopening costs, the effect of weather on
                  travel and transportation patterns, and local, national and
                  international economic conditions;

         -        the ability of the Company to form and maintain its strategic
                  relationships with certain large real estate owners and
                  operators;

         -        the ability of the Company to successfully implement Year 2000
                  compliance measures;

         -        global and/or regional economic factors and potential changes
                  in laws and regulations, including, without limitation,
                  changes in federal, state and international laws regulating
                  the environment;

         -        a significant delay in the expected closing of the proposed
                  merger with Allright.

OVERVIEW

         The Company operates parking facilities under three types of
arrangements: leases, fee ownership, and management contracts.

         Parking revenues consist of Central Parking Corporation and
subsidiaries ("Central Parking" or the "Company") revenues from leased and owned
facilities. Cost of parking relates to both leased and owned facilities and
includes rent, payroll and related benefits, depreciation (if applicable),
maintenance, insurance, and general operating expenses. Parking revenues in the
first quarter of fiscal 1999 increased to $99.6 million from $59.0 million in
the same quarter of fiscal 1998, an increase of $40.6 million, or 68.9%.

         Parking revenues from owned properties amounted to $5.0 million and
$3.7 million for the fiscal quarters ended December 31, 1998 and 1997,
respectively. Owned properties parking revenues, as a percentage of parking
revenues, accounted for 5.0% and 6.3% in the quarters ended December 31, 1998
and 1997, respectively. Ownership of parking facilities, either independently or
through joint ventures, typically requires a larger capital investment than
managed or leased facilities but provides maximum control over the operation of
the parking facility and the greatest profit potential of the three types of
operating arrangements. As the owner, all changes in owned facility revenue and
expense flow directly to the Company. Additionally, the Company has the
potential to realize benefits of appreciation in the value of the underlying
real estate if the property is sold. Central Parking assumes complete
responsibility for all aspects of the property, including all structural,
mechanical, or electrical maintenance or repairs and property taxes.



                                 Page 10 of 16
<PAGE>   11


         Parking revenues from leased facilities amounted to $94.6 million and
$55.3 million for the first fiscal quarters of 1999 and 1998, respectively.
Leased properties parking revenues, as a percentage of parking revenues,
accounted for 95.0% and 93.7% in the first quarters of 1999 and 1998,
respectively. Leases generally provide for a contractually established payment
to the facility owner which is either a fixed annual amount, a percentage of
gross revenues, or a combination thereof. As a result, Central Parking's
revenues and profits in its lease arrangements are dependent upon the
performance of the facility. Leased facilities require a longer commitment and a
larger capital investment by Central Parking than managed facilities but
generally provide a more stable source of revenue and a greater opportunity for
long-term revenue growth. Under its leases, the Company is typically responsible
for all facets of the parking operations, except for structural, mechanical, or
electrical maintenance or repairs, or property taxes. Lease arrangements are
typically for terms of three to ten years, with renewal options.

         Management contract revenues include revenues from managed facilities.
In the first fiscal quarter of 1999, management contract revenues increased
34.5% to $15.1 million over the same quarter in 1998. This increase is primarily
as a result of the addition of 207 managed facilities acquired in the
transactions with Kinney, Turner, and Sterling, and from the net addition of 105
additional management locations. Management contract revenues amounted to $15.1
million and $11.3 million for the quarters ended December 31, 1998 and 1997,
respectively. Management contract revenues consist of management fees (both
fixed and percentage of revenues) and fees for ancillary services such as
insurance, accounting, equipment leasing, and consulting. The cost of management
contracts includes insurance premiums and claims and other indirect overhead.
The Company's responsibilities under a management contract as a facility manager
include hiring, training, and staffing parking personnel, and providing
collections, accounting, record keeping, insurance, and facility marketing
services. In general, Central Parking is not responsible under its management
contracts for structural, mechanical, or electrical maintenance or repairs, or
for providing security or guard services or for paying property taxes. The
typical management contract is for a term of one to three years and generally is
renewable for successive one-year terms, but is cancelable by the property owner
on short notice.

         The Company's clients have the option of obtaining insurance on their
own or having Central Parking provide insurance as part of the services provided
under the management contract. Because of its size and claims experience, the
Company can purchase such insurance at discounts to comparable market rates and,
management believes, at lower rates than the Company's clients can generally
obtain on their own. Accordingly, Central Parking generates profits on the
insurance provided under its management contracts.

         As of December 31, 1998, Central Parking operated 1,307 parking
facilities through management contracts, leased 1,054 parking facilities, and
owned 68 parking facilities, either independently or in joint venture with third
parties.

Three Months Ended December 31, 1998 Compared to Three Months Ended December 31,
1997

Parking revenues for the first quarter of fiscal 1999 increased to $99.6 million
from $59.0 million in the first quarter of fiscal 1998, an increase of $40.6
million, or 68.9%. Of the $40.6 million increase, $34.0 million resulted from
the acquisitions of Kinney, Turner and Sterling's 251 leased and owned
locations. The remaining increase of $6.6 million, resulted from the net
addition of 32 leased and owned locations over the same quarter last year as
well as a combination of rate increases and higher utilization of parking spaces
at existing facilities. The Company converted four previously leased locations
to a management agreement. This conversion reduced parking revenues by $3.3
million in the first quarter of fiscal 1999 as compared to the same quarter of
fiscal 1998. Revenues from foreign operations amounted to $5.5 million and $5.6
million, for the quarters ended December 31, 1998 and 1997, respectively.

Management contract revenues for the first quarter of fiscal 1999 increased to
$15.1 million from $11.3 million in the first quarter of fiscal 1998, an
increase of $3.8 million or 34.5%. Of the $3.8 million increase, $1.6 million
resulted from the addition of 207 management locations through the acquisitions
of Kinney, Turner, and Sterling. The remaining increase of $2.2 million is
attributed to the net addition of 105 management contracts and increased
management fees on existing locations.

Cost of parking in the first quarter of 1999 increased to $81.7 million from
$51.0 million in the same quarter of 1998, an increase of $30.7 million or
60.4%. Rent expense increased $17.7 million from the first quarter of 1998 to
the first quarter of 1999, principally as a result of new locations from
acquisitions. Payroll increased $7.7 million from the quarter ended December 31,
1997 over the same period in 1998, principally as a result of new locations from
acquisitions and increases on existing locations. Cost of parking as a
percentage of parking revenues, decreased to 82.0% in the first quarter of
fiscal 1999 from 86.4% in fiscal first quarter 1998. This decrease was
attributable to lower




                                 Page 11 of 16
<PAGE>   12


operating costs such as rent and utilities associated with properties acquired
with Kinney, as well as the spreading of a number of other fixed costs, over a
larger revenue base. Additionally, as discussed above, the Company's conversion 
of four previously leased locations to a management agreement reduced costs of 
parking by $3.3 million in the first quarter of fiscal 1999 as compared to the 
same quarter of fiscal 1998.

Cost of management contracts in fiscal first quarter 1999 increased to $4.6
million from $3.3 million in the comparable period in 1998, an increase of $1.3
million or 42.2%. The increase in cost reflects higher insurance claims, in
total, and as a percentage of management contract revenue, and higher employment
taxes associated with the increase in the number of managed facilities. Cost of
management contracts as a percentage of management contract revenue increased to
30.5% for the first fiscal quarter 1999 from 28.9% for the same period last
year. 

General and administrative expenses excluding amortization of goodwill increased
to $10.3 million for the first quarter of fiscal 1999 from $6.6 million in
fiscal first quarter 1998, an increase of $3.7 million or 55.7%. The increase is
primarily attributable to the purchase of Kinney and the increased
administrative activities associated with the resultant business growth. General
and administrative expenses, as a percentage of revenues, were 9.0% for the
first quarter of fiscal 1999 compared to 9.4% for the first quarter of fiscal
1998. The decrease was attributable to spreading fixed expenses over a broader
base, and increased economies of scale as duplicate expenses associated with the
above acquisitions were eliminated.

Goodwill and non-compete amortization for the first quarter of fiscal 1999
increased to $2.6 million from $597 thousand in fiscal first quarter 1998, an
increase of $2.0 million, as a result of the Sterling, CPS of Louisiana, Turner,
and Kinney acquisitions.

Interest income increased to $826 thousand for the first quarter of fiscal 1999,
from $497 thousand in the first quarter of fiscal 1998, an increase of $329
thousand. The increase in interest income is a result of larger balances in
notes receivable outstanding during the quarter.

Interest expense decreased to $1.2 million for the first quarter of fiscal 1999
from $1.4 million in the first quarter of fiscal 1998. The decrease in interest
expense was primarily attributable to the decrease in indebtedness under the
Company's credit facilities. The weighted average balance outstanding under such
credit facilities was $47.0 million during the quarter ended December 31, 1998,
at a weighted average interest rate of 6.24%. The weighted average balance
outstanding was $78.5 million during the quarter ended December 31, 1997, at an
average interest rate of 6.6%. Additionally, the Company recorded dividends on
Company-obligated mandatorily redeemable securities of a subsidiary trust in the
amount of $1.4 million during the quarter ended December 31, 1998.

Income taxes increased to $5.9 million for the first quarter of fiscal 1999 from
$3.5 million in the first fiscal quarter in 1998, an increase of $2.4 million or
71.0%. The effective tax rate for the first fiscal 1999 quarter was 40.0%
compared to 38.0% for the 1998 quarter. The increase in the effective tax rate
is attributable to a combination of decreasing interest income on tax-exempt
investments, an increase in non-tax deductible goodwill amortization and an
increase in effective state income tax rates.

Liquidity and Capital Resources

         Operating activities for the first quarter of fiscal 1999 neither used
nor provided significant cash during the quarter ended December 31, 1998. Net
earnings of $8.9 million were offset by increases in current assets and
liabilities for the first fiscal quarter of 1999. $11.2 million in cash was
provided by operating activities during the same period in fiscal 1998. The
primary factors which contributed to this change were increases in the balances
of accounts receivable, management accounts receivable, prepaid expenses and
other assets during the quarter ended December 31, 1998. These increases were
due principally to the difference in the timing of the collection cycle in the
quarter ended December 31, 1998, and the overpayment of estimated federal income
taxes.

         Net cash used in investing activities was $4.9 million for the first
quarter of fiscal 1999, a decrease of $9.4 million from net cash of $14.3
million used in investing activities during the same quarter of fiscal 1998. The
primary factors which contributed to the decrease in cash used are; the
acquisition of Diplomat during the quarter ended December 31, 1997, which
utilized cash of $12.3 million, net of cash acquired, while the Company made no
acquisitions during the same quarter of the current fiscal year, partially
offset by increases in property and equipment purchases during the quarter ended
December 31, 1998 of $2.8 million over the same quarter last year.

         Net cash provided by financing activities for the quarter ended
December 31, 1998 was $4.9 million, a decrease of $1.4 million over the $6.3
million provided during the quarter ended December 31, 1997. Primary factors
which




                                 Page 12 of 16
<PAGE>   13


contributed to this decrease are decreased net borrowings under the revolving
credit agreement, and increased principal repayments on notes payable.

         Depending on the timing and magnitude of the Company's future
investments (either in the form of leased or purchased properties, joint
ventures, or acquisitions), the working capital necessary to satisfy current
obligations is anticipated to be generated from operations and Central Parking's
credit facility over the next twelve months. In the ordinary course of business,
Central Parking is required to maintain and, in some cases, make capital
improvements to the parking facilities it operates; however, as of December 31,
1998, Central Parking had no material outstanding commitments for capital
expenditures. If Central Parking identifies investment opportunities requiring
cash in excess of Central Parking's cash flows and the existing credit facility,
Central Parking may seek additional sources of capital, including the sale or
issuance of Central Parking common stock or convertible securities, or amending
the credit facility to obtain additional indebtedness. Central Parking's ability
to raise additional capital by issuing additional shares of common stock is
expected to be limited as a result of the registration rights agreement entered
into in connection with the pending merger with Allright Holdings, Inc.
("Allright"). The registration rights agreement provides certain limitations and
restrictions upon Central Parking's ability to issue new shares of Company
common stock. While Central Parking does not expect this limitation to affect
its working capital needs, it could have an impact on Central Parking's ability
to complete significant acquisitions.

         On February 11, 1998, Central Parking established a credit facility
providing for an aggregate availability of up to $300 million consisting of a
five-year $200 million revolving credit facility, including a sublimit of $25
million for standby letters of credit, and a $100 million five-year term loan
with scheduled repayments of $25 million per year, beginning in year two (the
"Credit Facility"). On March 18, 1998, the Company completed offerings of equity
and convertible trust issued preferred securities, from which the Company
obtained $195.6 million in net proceeds. The Company repaid and terminated the
$100 million term loan with proceeds from these offerings. The remaining $95.6
million in proceeds was applied to reduce the outstanding balance under the $200
million revolving credit facility. The Credit Facility bore interest until June
30, 1998 at a rate of LIBOR plus 1.25% On June 30, 1998, the interest rate on
the Credit Facility and the commitment fee on the unused portion reverted to a
grid pricing based on the achievement of various financial ratios. The Credit
Facility contains certain covenants including those that require Central Parking
to maintain certain financial ratios, restrict further indebtedness and limit
the amount of dividends payable. Central Parking used the Credit Facility to
replace the Company's prior revolving credit facility and to finance the Kinney
acquisition. At December 31, 1998, the amount outstanding under this Credit
Facility was $54.0 million and the interest rate was 6.45.% (LIBOR plus 75 basis
points). At December 31, 1998, Central Parking had available $138.7 million
under the Credit Facility.

         Convertible Trust Issued Preferred Securities and Equity Offerings

         On March 18, 1998, the Company completed an offering of 2,137,500
shares of common stock. The Company received net proceeds from the offering of
$89.1 million. Concurrent with the common stock offering, the Company created
the Trust which completed a private placement of 4,400,000 shares at $25.00 per
share of 5.25% convertible trust issued preferred securities pursuant to an
exemption from registration under the Securities Act of 1933, as amended. The
Preferred Securities represent preferred undivided beneficial interests in the
assets of Central Parking Finance Trust, a statutory business trust formed under
the laws of the State of Delaware. The Company owns all of the common securities
of the Trust. The Trust exists for the sole purpose of issuing the Preferred
Securities and investing




                                 Page 13 of 16
<PAGE>   14


the proceeds thereof in an equivalent amount of 5.25% Convertible Subordinated
Debentures ("Convertible Debentures") of the Company due 2028. The net proceeds
to the Company from the Preferred Securities private placement were $106.5
million. Each Preferred Security is entitled to receive cumulative cash
distributions at an annual rate of 5.25% (or $1.312 per share) and will be
convertible at the option of the holder thereof into shares of Company common
stock at a conversion rate of 0.4545 shares of Company common stock for each
Preferred Security (equivalent to $55.00 per share of Company common stock),
subject to adjustment in certain circumstances. The Preferred Securities do not
have a stated maturity date but are subject to mandatory redemption upon the
repayment of the Convertible Debentures at their stated maturity (April 1, 2028)
or upon acceleration or earlier repayment of the Convertible Debentures. The
proceeds of the equity and preferred security offerings were used to repay
indebtedness.

The Company's consolidated balance sheets reflect the Preferred Securities of
the Trust as company-obligated mandatorily redeemable convertible securities of
subsidiary whose assets are convertible subordinated debentures of the Parent.




                                 Page 14 of 16
<PAGE>   15



PART II - OTHER INFORMATION

Item 4.  Submission of Matters to a Vote of Security-Holders

There were no matters submitted to a vote of security-holders during the quarter
ended December 31, 1998, however on January 15, 1999, the Company mailed a joint
proxy statement/prospectus to its shareholders regarding the proposed merger
with Allright Holdings, Inc. ("Allright"). The date of the special meeting of
shareholders to vote on the merger is February 17, 1999.

Item 6.  Exhibits and Reports on Form 8-K

         (a)      Exhibits

27.      Financial Data Schedule (EDGAR Filing Only)

         (b)      Reports on Form 8-K

         The Company filed a Current Report on Form 8-K on November 23, 1998
         announcing preliminary results for fiscal 1998.

         The Company filed a Current Report on Form 8-K on December 4, 1998
         announcing operating results for fiscal 1998.

         The Company filed a Current Report on Form 8-K on February 12, 1999
         announcing operating results for the first quarter of fiscal 1999.




                                 Page 15 of 16
<PAGE>   16



                                   SIGNATURES

Pursuant to the requirements of Section 13 or 15(d) of the Securities Exchange
Act of 1934, the Registrant has duly caused this report to be signed on its
behalf by the undersigned, thereunto duly authorized.

                                    CENTRAL PARKING CORPORATION


Date: February 15, 1999             By: /s/ Stephen A. Tisdell
     --------------------              ----------------------------------
                                        Stephen A. Tisdell
                                        Chief Financial Officer

         Pursuant to the requirements of the Securities Exchange Act of 1934,
this report has been signed below by the following persons on behalf of the
Registrant in the capacities and on the dates indicated.

<TABLE>
<CAPTION>
           Signature                                          Title                                Date
<S>                                             <C>                                                <C>
                                                Chief Financial Officer (Principal
          /s/ Stephen A. Tisdell                Financial and Accounting Officer)
-------------------------------------------
            Stephen A. Tisdell
</TABLE>



                                 Page 16 of 16