<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                                   FORM 10-Q/A

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

                  FOR THE QUARTERLY PERIOD ENDED JUNE 30, 1998

                                       or

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

                         COMMISSION FILE NUMBER 0-25202

                                KITTY HAWK, INC.
             (Exact name of registrant as specified in its charter)

       Delaware                                         75-2564006
(State of Incorporation)                    (I.R.S. Employer Identification No.)

                              1515 West 20th Street
                                 P.O. Box 612787
              Dallas/Fort Worth International Airport, Texas 75261
                                 (972) 456-2200
               (Address, including zip code, and telephone number,
       including area code, of registrant's principal executive offices)

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 [ ]

                                       1

<PAGE>   2



    The following paragraph amends and restates in its entirety the fourth
paragraph under the heading Liquidity and Capital Resources.

    The Company has a $45.9 million outstanding Term Loan. The Term Loan is due
in quarterly installments of $2.25 million commencing in March 1999, with the
balance of $12.15 million due upon maturity in September 2002. Interest on the
Term Loan accrues at LIBOR plus 3% or a Base Rate plus 1.5%, subject to
reduction. The Base Rate is the higher of the Prime Rate of Wells Fargo Bank,
N.A. ("WFB") or the Federal Funds Rate plus .5%. As of June 30, 1998, the
interest rate was 7.95%. The Term Loan is secured by accounts receivable, all
spare parts (including rotables), inventory, intangibles and contract rights,
cash, 16 Boeing 727s and related engines and the stock of each of the Company's
subsidiaries, not including the Company's 60% interest in AIC. The Term Loan is
guaranteed by all of the Company's subsidiaries, other than AIC.


                                       2

<PAGE>   3



SIGNATURES

    Pursuant to the requirements of the Securities Exchange Act of 1934, the
Company has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized, on September 3, 1998.

                                         KITTY HAWK, INC.


                                         By: /s/ RICHARD R. WADSWORTH
                                             -------------------------------
                                             Richard R. Wadsworth, Jr.
                                             Senior Vice President - Finance,
                                             Chief Financial Officer, and 
                                             Secretary



                                       3