<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D. C. 20549


                                    FORM 10-Q


               QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF
                       THE SECURITIES EXCHANGE ACT OF 1934



   For the Quarterly Period Ended April 2, 1999 Commission File Number 0-14759
                                  -------------                        -------



                          KLLM TRANSPORT SERVICES, INC.
             ------------------------------------------------------
             (Exact name of registrant as specified in its charter)


                Delaware                                 64-0412551  
                --------                                 ----------  
     (State or other jurisdiction of                   (I.R.S. Employer
     incorporation or organization)                    Identification No.)



           135 Riverview Drive
           Richland, Mississippi                           39218  
           ---------------------                           -----  
  (Address of principal executive offices)               (Zip Code)


        Registrant's telephone number, including area code (601) 939-2545
                                                           --------------


      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, and (2) has been subject to such filing
requirements for the past 90 days.
                                            Yes  X       No      
                                                --- 
                                        



      4,092,525 Common Shares were outstanding as of April 2, 1999.



<PAGE>   2




                          KLLM TRANSPORT SERVICES, INC.
                                AND SUBSIDIARIES


                                      INDEX


<TABLE>
<CAPTION>
                                                                                                                       Page
                                                                                                                      Number
                                                                                                                      ------
    <S>                                                                                                               <C>
    PART I.     FINANCIAL INFORMATION:

       Item 1.  Financial Statements

                       Condensed Consolidated Balance Sheets
                          April 2, 1999 (Unaudited) and January 1, 1999                                                   1

                       Consolidated Statements of Earnings (Unaudited)
                          Thirteen weeks ended April 2, 1999 and
                          April 3, 1998                                                                                   2

                       Condensed Consolidated Statements of Cash Flows (Unaudited)
                          Thirteen weeks ended April 2 1999 and April 3, 1998                                             3

                       Notes to Condensed Consolidated Financial Statements (Unaudited)                                   4

       Item 2.  Management's Discussion and Analysis of Financial Condition and Results of Operations                     5

       Item 3.  Quantitative and Qualitative Disclosures about Market Risk                                                7

    PART II.    OTHER INFORMATION:

       Item 6.  Exhibits and Reports on Form 8-K                                                                          8
</TABLE>



<PAGE>   3
                         KLLM TRANSPORT SERVICES, INC.
                                AND SUBSIDIARIES
                     CONDENSED CONSOLIDATED BALANCE SHEETS


<TABLE>
<CAPTION>
                                                                                    April 2,                    January 1,
                                                                                      1999                         1999
                                                                                    -----------                 -----------
                                                                                    (Unaudited)                   (Note)
                                                                                                  (In thousands)
                                                       ASSETS
<S>                                                                                 <C>                         <C>
Current assets:
 Cash and cash equivalents                                                          $    674                   $     756
 Accounts receivable                                                                  21,541                      21,132
 Inventories - at cost                                                                   633                         597
 Prepaid expenses:
   Tires                                                                               2,660                       2,758
   Other                                                                               4,202                       2,490
 Assets held for sale                                                                  1,530                       1,530
 Deferred income taxes                                                                 5,818                       5,818
                                                                                    --------                    --------
    Total current assets                                                              37,058                      35,081


Property and equipment                                                               135,407                     131,953
 Less accumulated depreciation                                                       (37,087)                    (33,741)
                                                                                    --------                    --------
                                                                                      98,320                      98,212

Other assets                                                                              22                          69
                                                                                    --------                    --------
                                                                                    $135,400                    $133,362
                                                                                    --------                    --------

                                       LIABILITIES AND STOCKHOLDERS' EQUITY

Current liabilities:
 Note payable to bank                                                               $  2,212
 Accounts payable and accrued expenses                                                 9,377                     $ 11,745
 Accrued claims expense                                                               14,405                       15,041
 Current maturities of long-term debt
  and capital leases                                                                   2,857                        2,857
                                                                                    --------                     --------
    Total current liabilities                                                         28,851                       29,643

Long-term debt and capital leases, less
 current maturities                                                                   40,571                       36,571

Deferred income taxes                                                                 14,480                       14,480

Stockholders' equity:
 Preferred Stock, $.01 value; authorized 5,000,000 shares; none issued
 Common Stock $1 par value; 10,000,000 shares authorized;
  issued shares - 4,558,754 in 1999 and 1998:
  outstanding shares - 4,092,525 in 1999 and 4,224,488 in 1998.                        4,559                        4,559
 Additional paid-in capital                                                           32,852                       32,858 
 Retained earnings                                                                    18,344                       18,569
                                                                                    --------                     --------
                                                                                      55,755                       55,986
 Less common stock in treasury, at cost, 466,229 shares
  in 1999 and 334,266 shares in 1998, at cost                                         (4,257)                      (3,318)
                                                                                    --------                     -------- 
    Total stockholders' equity                                                        51,498                       52,668
                                                                                    --------                     --------
                                                                                    $135,400                     $133,362
                                                                                    ========                     ========
</TABLE>

Note: The balance sheet at January 1, 1999 has been derived from the audited
financial statements at the date indicated, but does not include all of the
information and footnotes required by generally accepted accounting principles
for complete financial statements.

See accompanying notes. 
<PAGE>   4

                         KLLM TRANSPORT SERVICES, INC.
                                AND SUBSIDIARIES
                      CONSOLIDATED STATEMENTS OF EARNINGS
                                  (UNAUDITED)


<TABLE>
<CAPTION>
                                                              Thirteen Weeks Ended
                                                           April 2,             April 3,
                                                             1999                 1998
                                                   -------------------------------------------------
                                                   (In Thousands, Except Share and Per Share Amount)
<S>                                                <C>                       <C>
OPERATING REVENUE                                      $    55,331          $    59,190

OPERATING EXPENSES:
 Salaries, wages and
  fringe benefits                                           19,342               19,756
 Operating supplies
  and expenses                                              13,146               14,331
 Insurance, claims,
  taxes and licenses                                         3,143                3,250
 Depreciation and
  amortization                                               4,367                4,660
 Purchased transportation
  and equipment rent                                        12,351               12,736
 Other                                                       2,679                2,729
 Gain on sale of
  revenue equipment                                           (117)                  (2)
                                                       -----------          -----------
  TOTAL OPERATING EXPENSES                                  54,911               57,460
                                                       -----------          -----------

  OPERATING INCOME                                             420                1,730

Interest and other income                                       (8)                (907)
Interest expense                                               803                  956
                                                       -----------          -----------
                                                               795                   49
                                                       -----------          -----------

EARNINGS (LOSS) BEFORE INCOME TAXES                           (375)               1,681
Income tax (benefit) expense                                  (150)                 675
                                                       -----------          -----------

NET EARNINGS (LOSS)                                    $      (225)         $     1,006
                                                       ===========          ===========

BASIC AND DILUTED EARNINGS (LOSS) PER COMMON SHARE     $     (0.05)         $      0.23
                                                       ===========          ===========

WEIGHTED AVERAGE NUMBER OF SHARES OUTSTANDING            4,179,059            4,373,115
                                                       ===========          ===========

</TABLE>

See accompanying notes.



                                       2
<PAGE>   5
                         KLLM TRANSPORT SERVICES, INC.
                                AND SUBSIDIARIES
                CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                                  (UNAUDITED)


<TABLE>
<CAPTION>
                                                                        Thirteen Weeks Ended
                                                                      April 2,        April 3,
                                                                        1999            1998
                                                                      -----------------------
                                                                           (In Thousands)
<S>                                                                 <C>                <C>
NET CASH PROVIDED BY (USED IN) OPERATING ACTIVITIES                 $ (892)            $2,276

CASH FLOWS FROM INVESTING ACTIVITIES:
  Purchases of property and equipment                                (7,034)             (420)
  Proceeds from disposition of property, equipment and
    assets held for sale                                              2,592             3,184
                                                                    -------            ------
NET CASH FLOWS PROVIDED BY (USED IN) INVESTING ACTIVITIES            (4,442)            2,764


CASH FLOWS FROM FINANCING ACTIVITIES:
  Purchases of common stock for treasury                               (960)                0
  Net increase (decrease) in borrowings under
    revolving line of credit                                          4,000            (6,000)
  Repayment of long-term debt and capital leases                          0              (193)
  Net change in borrowings under working capital
    line of credit                                                    2,212             1,190
                                                                    -------            ------
NET CASH FLOWS PROVIDED BY (USED IN)
  FINANCING ACTIVITIES                                                5,252            (5,003)
                                                                    -------            ------

Net increase (decrease) in cash and
  cash equivalents                                                      (82)               37
Cash and cash equivalents at beginning
  of period                                                             756               670
                                                                    -------            ------
Cash and cash equivalents at end of period                          $   674            $  707
                                                                    =======            ======

NONCASH FINANCING ACTIVITIES
  Common stock issued for services                                  $    15            $    0
                                                                    =======            ======
</TABLE>
See accompanying notes.

                                       3
<PAGE>   6



                         KLLM TRANSPORT SERVICES, INC.
                                AND SUBSIDIARIES
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                   (Unaudited)



NOTE A-BASIS OF PRESENTATION

         The accompanying unaudited condensed consolidated financial statements
have been prepared in accordance with generally accepted accounting principles
for interim financial information. They have been prepared in accordance with
the instructions to Form 10-Q and Article 10 of Regulation S-X and accordingly,
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.

         In June 1998, the FASB issued Statement of Financial Accounting
Standards No. 133, "Accounting for Derivative Instruments and Hedging
Activities" (SFAS No. 133). The provisions of SFAS No. 133 require all
derivatives to be recorded on the balance sheet at fair value. SFAS No. 133
establishes "special accounting" for fair value hedges, cash flow hedges, and
hedges of foreign currency exposures of net investments in foreign operations.
Derivatives that are not hedges must be adjusted to fair value through income.
If the derivative is a hedge, depending on the nature of the hedge, changes in
the fair value of derivatives will either be offset against the change in fair
value of the hedged item through earnings or recognized in other comprehensive
income until the hedged item is recognized in earnings. Management expects the
effect of the adoption of this statement will be insignificant to the earnings
and financial position of the Company when it becomes effective for fiscal 2000.


NOTE B-FISCAL YEAR

         The Company has adopted a fiscal year-end on the Friday nearest
December 31. Accordingly, the first quarter of 1999 ended on Friday, April 2,
1999.


NOTE C-COMMITMENTS AND CONTINGENCIES

         The Company is involved in various claims and routine litigation
incidental to its business. Management is of the opinion that the outcome of
these matters will not have a material adverse effect on the consolidated
financial position or results of consolidated operations of the Company.

         To hedge its exposure to price fluctuations, the Company periodically
enters into heating oil (diesel fuel) swap agreements. Agreements to purchase
12% of the remaining 1999 anticipated fuel requirements and approximately 1% of
its 2000 anticipated fuel requirements were in place at the end of the quarter.
Such agreements are settled monthly and are accounted for as hedges with gains
and losses recognized in operating expenses using the accrual method as part of
the fuel cost over the hedge period. The Company does not engage in speculative
transactions nor does the company hold or issue derivative instruments for
trading purposes.


                                        4

<PAGE>   7



ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
         RESULTS OF OPERATIONS


RESULTS OF OPERATIONS

         A series of freezes in California in December and early January
severely damaged the citrus crop, resulting in excess temperature-controlled
trucking capacity in January and February. In addition, late winter storms in
the Midwest and Northeast delayed shipments of nursery stock that normally occur
in March. These conditions had a negative effect on temperature-controlled
freight demand and resulted in a higher percentage of empty miles driven, a
lower average rate per mile, and lower utilization of equipment. Dry freight
services were not affected by West Coast weather.

         Operating revenue for the first quarter of 1999 decreased 6.5% from the
comparable period of 1998. The decrease in operating revenue in the first
quarter consisted of a 10.3% decrease from the Company's traditional over-the-
road temperature-controlled freight services, net of a 3.8% increase from the
dry-van over-the-road truckload division. The average revenue per mile decreased
from $1.12 to $1.11 for the first quarter of 1999 as compared to the same period
in 1998. There were no fuel surcharges in either period.

         The impact of the winter weather had an adverse effect on profitability
in the first quarter. The operating ratio increased from 97.1% to 99.2% for the
first quarter of 1999 compared to the same period in 1998.

         During the third quarter of 1998, the Company implemented a
restructured pay package that increased compensation for certain drivers. That
increase partially offsets the decrease in driver compensation resulting from
fewer miles driven during the quarter when compared to the same period last
year. Operating supplies and expenses decreased $1,185,000 in the first quarter
compared to the same period last year primarily due to lower fuel prices
($795,000) and various cost control efforts. For the first quarter of 1999,
insurance, claims, taxes and licenses are $107,000 below the first quarter of
1998. Depreciation and amortization for the first quarter of 1999 were $293,000
below the same period last year due to a shift from the purchase of equipment to
operating leases for certain revenue equipment acquired in 1998. As a result of
that shift, purchased transportation and equipment rent did not decrease at the
same rate as revenue. The Company's equipment trade cycle resulted in a gain on
the disposition of revenue equipment of $117,000, an increase of $115,000 over
the same period in 1998.

         As a result of the foregoing, operating income decreased by $1,310,000
for the first quarter of 1999 when compared to the comparable period of 1998.
Other income was $899,000 greater last year as a result of the sale of the
corporate office building during the first quarter of 1998.

         Net income for the first quarter of 1999 decreased $1,231,000 compared
to the same period in 1998. Basic and diluted earnings (loss) per share
decreased from $.23 to $(.05) in the first quarter of 1999 compared to the same
period in 1998.


LIQUIDITY AND CAPITAL RESOURCES

         The Company's primary sources of liquidity are its cash flow from
operations and its existing credit agreements. During the thirteen weeks ended
April 2, 1999, the Company used $892,000 in net cash from operating activities.
In the first quarter of 1999 the Company purchased 18 month life truck tags. The
effect of this purchase was to use $1,400,000 in additional cash in the first
quarter which will be offset by reduced cash flow in future quarters.

         During the first three months of 1999, net capital resources required
by the Company were approximately $4.4 million. Net capital expenditures for the
remainder of 1999, primarily for revenue equipment, are expected to be
approximately $24 million although management may finance a portion of the
capital expenditures with operating leases. The Company has entered into
operating leases for 200 trailers during the first quarter and has plans to
lease an additional 400 throughout the rest of 1999.

         The Company has a $50,000,000 unsecured revolving line of credit with a
syndication of banks. Borrowings of $32,000,000 were outstanding at April 2,
1999. Under the terms of the agreement, borrowings bear interest at (i) the
higher of prime rate or a rate based upon the Federal Funds Effective Rate, (ii)
a rate based upon the Eurodollar rates, or (iii) an absolute interest rate as
determined by each lender in the syndication under a competitive bid process at
the Company's option. Facilities fees from 1/5% to 3/8% per annum are charged on
the unused portion of this line. At April 2, 1999, the aggregate principal
amount of the Company's outstanding long-term indebtedness was approximately
$43.4 million. Of this total outstanding, $11.4 million was in the form of 9.11%
senior notes due June 2002 and $32.0 

                                        5

<PAGE>   8
million consisted of the revolving line of credit due April 2000.

         Working capital needs have generally been met from net cash provided
from operating activities. The Company has a $4 million unsecured working
capital line of credit with a bank, $1.7 million of which was available at April
2, 1999. Interest is at a rate based upon the Eurodollar rates with facility
fees at 1/4% per annum on the unused portion of the line.

         During 1998, the Company announced plans to purchase up to 150,000
shares of the Company's outstanding stock in the first quarter. During the
quarter, 134,000 shares were repurchased for $960,000.

         The Company anticipates that its existing credit facilities along with
cash flow from operations will be sufficient to fund operating expenses, capital
expenditures, debt service, and any additional stock repurchases.


IMPACT OF YEAR 2000

         Some of the Company's older computer programs were written using two
digits rather than four to define the applicable year. As a result, those
computer programs have time-sensitive software that recognizes a date using "00"
as the year 1900 rather than the year 2000. This date problem could cause a
system failure or could cause miscalculations which would disrupt operations,
including, among other things, a temporary inability to process transactions,
send invoices, or engage in similar normal business activities. During 1999 the
Company has progressed with modifications to its computer software which will
enable its computer systems to function properly with respect to dates in the
year 2000 and thereafter. The failure of the Company, its suppliers, or its
customers to adequately prepare for the year 2000 problem could have an adverse
affect on the consolidated financial results of consolidated operations of the
Company.

         Beginning in mid 1996, the Company established a conversion timeline.
Each software system was identified and categorized as year 2000 ready,
not-ready and conversion planned, and not-ready with replacement planned. During
the two and one-half years since that study, the conversion effort and timeline
has been updated to reflect progress on the overall project. Consistent with the
original year 2000 conversion timeline, the project is approximately eighty-five
percent complete. At present, management of the Company believes that sufficient
resources are in place to complete the effort by June 30, 1999. Upon completion
of the effort, detail testing, including actually changing the date to the year
2000 in certain systems, will be performed to ensure a seamless passage into the
year 2000. The total project is estimated at approximately $700,000 for the
purchase of new software and the modification of existing software with $400,000
of the total capitalized and the remaining $300,000 expensed as incurred.
Through April 2, 1999, approximately $280,000 had been capitalized and $200,000
had been expensed. Over the three year project, approximately 10% of the
information systems budget will be directed to Year 2000 compliance.

         To determine the scope of the effort beyond the Company's systems, each
operating department of the Company is determining the population of significant
suppliers and their level of preparedness. In certain applications, tests have
been performed to ensure an uneventful continuation of business. The Company's
suppliers, vendors, and equipment manufacturers, have indicated that they
continue to assess the impact of the Year 2000 on their operations. In the event
of an unforeseen problem, the Company is studying contingency plans that may
include communication with drivers other than via satellite and manual
transactions. If certain suppliers such as fuel vendors are unable to supply
products or if customer locations are closed due to their inability to operate,
the Company's operations could be suspended. Although management has been
assured that revenue equipment will not be affected, a Year 2000 electronic
malfunction could render certain pieces of equipment inoperable.

         The Company's diverse customer base provides assurance that the
inability of one customer to operate, due to Year 2000 related problems, will
not have a significant adverse impact on the operations of the Company.


FACTORS AFFECTING FUTURE PERFORMANCE

         The Company's future operating results may be affected by various
trends and factors which are beyond the Company's control. These include adverse
changes in demand for trucking services, availability of drivers and fuel
prices. Accordingly, past performance should not be presumed to be an accurate
indication of future performance.


                                       6

<PAGE>   9

SEASONALITY

         In the transportation industry, results of operations generally show a
seasonal pattern because customers reduce shipments during and after the winter
holiday season with its attendant weather variations. The Company's operating
expenses have historically been higher in the winter months primarily due to
decreased fuel efficiency and increased maintenance costs in colder weather.


ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK


MARKET RISK

         Market risk relating to the Company's operations result primarily from
changes in interest rates and the price of heating oil (diesel fuel), as well as
credit risk concentration. The Company does not use financial instruments for
trading purposes and is not a party to any leveraged derivatives.

         The Company's interest expense is sensitive to changes in the general
level of U. S. interest rates. The Company also maintains certain components of
its debt as fixed rate in nature to mitigate the impact of fluctuations in
interest rates.



                                        7

<PAGE>   10



PART II: OTHER INFORMATION

Item 6.  Exhibits and Reports on Form 8-K

         Exhibit 27 - Financial Data Schedule

         There were no Form 8-K filings for the quarter ended April 2, 1999.


                                        8

<PAGE>   11


SIGNATURES

Pursuant to the requirements 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.




                                        KLLM TRANSPORT SERVICES, INC.
                                        -----------------------------
                                                 (Registrant)


Date      May 17, 1999           /s/  Jack Liles
    ------------------          -------------------------------------------
                                 Jack Liles
                                 Chairman of the Board, President and Chief
                                 Executive Officer



Date      May 17, 1999             /s/ Steven L. Dutro      
    ------------------           -----------------------------------------
                                 Steven L. Dutro
                                 Senior Vice President and Chief Financial
                                 Officer