<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   March 31, 2000  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
                                                            ---             ---




         4,101,468 Common Shares were outstanding as of March 31, 2000.
<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
                     March 31, 2000 (Unaudited) and December 31, 1999                                       1

                   Consolidated Statements of Earnings (Unaudited)
                     Thirteen weeks ended March 31, 2000 and
                     April 2, 1999                                                                          2

                   Condensed Consolidated Statements of Cash Flows (Unaudited)
                     Thirteen weeks ended March 31, 2000 and April 2, 1999                                  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                                  6

    PART II.  OTHER INFORMATION:

       Item 6.  Exhibits and Reports on Form 8-K                                                            7
</TABLE>
<PAGE>   3
                          KLLM TRANSPORT SERVICES, INC
                                AND SUBSIDIARIES
                      CONDENSED CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                                 March 31,      December 31,
                                                                                   2000            1999
                                                                                 ---------      ------------
                                                                                (Unaudited)       (Note)
                                                                                       (In thousands)
<S>                                                                              <C>              <C>
                               ASSETS
Current assets:
     Cash and cash equivalents                                                   $   1,618        $     511
     Accounts receivable                                                            23,677           26,704
     Inventories - at cost                                                             715              686
     Prepaid expenses:
          Tires                                                                      3,700            3,625
          Other                                                                      1,911            3,474
     Deferred income taxes                                                           5,101            5,101
                                                                                 ---------        ---------
               Total current assets                                                 36,722           40,101

Property and equipment                                                             155,028          145,589
     Less accumulated depreciation                                                 (50,464)         (46,543)
                                                                                 ---------        ---------
                                                                                   104,564           99,046
                                                                                 ---------        ---------
                                                                                 $ 141,286        $ 139,147
                                                                                 =========        =========
             LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
     Notes payable to banks                                                      $   2,569
     Accounts payable and accrued expenses                                          17,722        $  14,032
     Accrued claims expense                                                         11,733           12,865
                                                                                 ---------        ---------
          Total current liabilities                                                 32,024           26,897

  Long-term debt, less current maturities                                           46,000           48,000

Deferred income taxes                                                               13,283           13,283

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 2000 and 1999;
       outstanding shares - 4,101,468 in 2000 and 4,098,967 in 1999                  4,559            4,559
     Additional paid-in capital                                                     32,808           32,822
     Retained earnings                                                              16,777           17,777
                                                                                 ---------        ---------
                                                                                    54,144           55,158
     Less common stock in treasury, 457,286 shares in 2000 and
      459,787 shares  in 1999, at cost                                              (4,165)          (4,191)
                                                                                 ---------        ---------
          Total stockholders' equity                                                49,979           50,967
                                                                                 ---------        ---------
                                                                                 $ 141,286        $ 139,147
                                                                                 =========        =========
</TABLE>

Note: The balance sheet at December 31, 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
                                                              ---------------------------------------------
                                                               March 31,                         April 2,
                                                                 2000                              1999
                                                              -----------                       -----------
                                                            (In Thousands, Except Share and Per Share Amounts)
<S>                                                         <C>                                 <C>
OPERATING REVENUE                                             $    57,593                       $    55,331

OPERATING EXPENSES:

    Salaries, wages and fringe benefits                            20,833                            19,342
    Operating supplies and expenses                                15,919                            13,146
    Insurance, claims, taxes and licenses                           2,745                             3,143
    Depreciation and amortization                                   4,885                             4,367
    Purchased transportation and equipment rent                    11,625                            12,351
    Other                                                           2,449                             2,679
    Gain on sale of revenue equipment                                (130)                             (117)
                                                              -----------                       -----------
    TOTAL OPERATING EXPENSES                                       58,326                            54,911
                                                              -----------                       -----------

    OPERATING INCOME (LOSS)                                          (733)                              420

Interest and other income                                             (51)                               (8)
Interest expense                                                      943                               803
                                                              -----------                       -----------
                                                                      892                               795
                                                              -----------                       -----------

EARNINGS (LOSS) BEFORE INCOME TAXES                                (1,625)                             (375)
Income tax (benefit) expense                                         (625)                             (150)
                                                              -----------                       -----------

NET EARNINGS (LOSS)                                           $    (1,000)                      $      (225)
                                                              ===========                       ===========


BASIC AND DILUTED EARNINGS (LOSS) PER COMMON SHARE            $     (0.24)                      $     (0.05)
                                                              ===========                       ===========


WEIGHTED AVERAGE NUMBER OF SHARES OUTSTANDING                   4,100,039                         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
                                                                                  March 31,       April 2,
                                                                                    2000           1999
                                                                                  --------        -------
                                                                                      (In Thousands)
<S>                                                                               <C>             <C>
NET CASH PROVIDED BY (USED IN) OPERATING
  ACTIVITIES                                                                      $ 10,929        $  (892)

CASH FLOWS FROM INVESTING ACTIVITIES:
  Purchases of property and equipment                                              (12,322)        (7,034)
  Proceeds from disposition of property, equipment and assets held for sale          1,931          2,592
                                                                                  --------        -------
NET CASH FLOWS USED IN INVESTING ACTIVITIES                                        (10,391)        (4,442)

CASH FLOWS FROM FINANCING ACTIVITIES:
  Purchases of common stock for treasury                                                 0           (960)
  Net change in borrowings under
    revolving line of credit                                                        (2,000)         4,000
  Net change in borrowings under working
    capital line of credit                                                           2,569          2,212
                                                                                  --------        -------
NET CASH FLOWS PROVIDED BY
  FINANCING ACTIVITIES                                                                 569          5,252
                                                                                  --------        -------


  Net Increase  (Decrease) in Cash and Cash Equivalents                              1,107            (82)

  Cash and Cash Equivalents at Beginning of Period                                     511            756
                                                                                  --------        -------

  Cash and Cash Equivalents at End of Period                                      $  1,618        $   674
                                                                                  ========        =======



NONCASH FINANCING ACTIVITIES
  Common stock issued for services                                                $     12        $    15
                                                                                  ========        =======
</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 results of
the consolidated operations and financial position of the Company when it
becomes effective for fiscal 2001.


NOTE B- FISCAL YEAR

         The Company has adopted a fiscal year-end on the Friday nearest
December 31. Accordingly, the first quarter of 2000 ended on Friday, March 31,
2000.


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
approximately 2% of the remaining anticipated fuel requirements for 2000 were in
place as of March 31, 2000. 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

         Operating revenue for the first quarter of 2000 increased 4% from the
comparable period of 1999 while the number of trucks in operation remained
fairly consistent. The increase in operating revenue in the first quarter
consisted of a 1% increase from the Company's traditional over-the-road
temperature-controlled freight services and a 3% increase from the dry-van
over-the-road truckload division and resulted from higher utilization of
equipment (3%) and an increase in average revenue per total mile (1%). Fuel
surcharges added $1,308,000 to operating revenues in the first quarter of 2000.
The Company had no fuel surcharges in the first quarter of 1999.

         The operating ratio increased from 99.2% to 101.2% for the first
quarter of 2000 compared to the same period in 1999. Fuel charges, within
operating supplies, were much higher than expected for the first quarter of
2000. Net of surcharges and fuel hedges, the higher fuel costs in the first
quarter of 2000 reduced operating income for the quarter by approximately
$1,800,000 compared to the same period in 1999. During the first quarter of
2000, many driver performance related expenses continued to improve, having the
effect of reducing operating supplies and insurance, taxes and licenses from the
levels in the prior year.

         As a result of the foregoing, operating income decreased by $1,153,000
for the first quarter of 2000 when compared to the comparable period of 1999.
For the first three months of 2000, interest expense was $140,000 more than last
year as a result of an increase in the level of debt and in the interest rates
charged on that debt.

         The net loss increased $775,000 for the first quarter of 2000 compared
to the same period in 1999. Basic and diluted earnings per share decreased $.19
to a loss of $.24 in the first quarter of 2000 compared to the same period in
1999.


LIQUIDITY AND CAPITAL RESOURCES

         The Company's primary sources of liquidity are cash flow from
operations and its existing credit agreements. During the thirteen weeks ended
March 31, 2000, the Company generated $10,929,000 in net cash from operating
activities.

         During the first three months of 2000, the Company's purchase of
equipment net of equipment sales were approximately $10 million. Net capital
expenditures for the remainder of 2000, primarily for revenue equipment, are
expected to be approximately $10 million.

         The Company has a $60,000,000 unsecured revolving line of credit (the
"Revolver") with a syndication of banks. Borrowings under the Revolver of
$46,000,000 were outstanding at March 31, 2000. Under the terms of the Revolver,
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 1/4% to 1/2% per annum are charged on the unused portion of this line.
At March 31, 2000, borrowings under the Revolver represented the Company's only
long-term debt outstanding.

         Working capital needs have generally been met from net cash provided
from operating activities. The Company has a $5 million unsecured working
capital line of credit with a bank, $2,431,000 of which was available at March
31, 2000. Interest is at a rate based upon the Eurodollar rates with facility
fees at 3/8% per annum on the unused portion of the line.

         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.


                                        5
<PAGE>   8
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.

         As described in the SEC filings made subsequent to the end of the first
quarter of 2000, a change in the control of the company is possible. The related
bidding process described in the filings is not complete.


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.


FORWARD LOOKING INFORMATION

         The foregoing statements contain forward-looking statements which
involve risks and uncertainties and the Company's actual experience may differ
materially from that discussed above. Factors that may cause such a difference
include, but are not limited to, those discussed in "Factors Affecting Future
Performance" as well as future events that have the effect of reducing the
Company's available cash balances, such as unanticipated operating losses or
capital expenditures related to possible future acquisitions. Readers are
cautioned not to place undue reliance on forward-looking statements, which
reflect management's analysis only as of the date hereof. The Company assumes no
obligation to update forward-looking statements.



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.


                                       6
<PAGE>   9
PART II:  OTHER INFORMATION

Item 6.  Exhibits and Reports on Form 8-K

         Exhibit 27 - Financial Data Schedule

             There was one Form 8-K filing for the quarter ended March 31,
2000. The 8K reported the election of a director and was filed on February 15,
2000.


                                       7
<PAGE>   10
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 12, 2000                  /s/ Jack Liles
                                     -------------------------------------
                                     Jack Liles
                                     Chairman of the Board, President and Chief
                                     Executive Officer



Date   May 12, 2000                  /s/ Steven L. Dutro
                                     -------------------------------------
                                     Steven L. Dutro
                                     Senior Vice President and Chief Financial
                                     Officer


                                       8