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

                                    FORM 10-Q


 X   QUARTERLY REPORT PURSUANT TO SECTION 13 or 15(d) OF THE SECURITIES
---  EXCHANGE ACT OF 1934
For the quarterly period ended April 29, 1998

                                                      OR

     TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
---  EXCHANGE ACT OF 1934
For the transition period from           to
                              -----------  -----------


Commission File No. 1-327
                   ------

                                KMART CORPORATION
             (Exact name of registrant as specified in its charter)


       Michigan                                                  38-0729500
--------------------------------------------------------------------------------
(State or other jurisdiction of                               (I.R.S. Employer
incorporation or organization)                               Identification No.)

3100 West Big Beaver Road - Troy, Michigan                          48084
--------------------------------------------------------------------------------
 (Address of principal executive offices)                         (Zip Code)

Registrant's telephone number, including area code              (248) 643-1000
                                                                ----------------


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
                              -------       -------


As of May 27, 1998, 492,348,167 shares of Common Stock of the Registrant were
outstanding.


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                                      INDEX

PART I            FINANCIAL INFORMATION                                     PAGE

Item 1.           Financial Statements


                  Consolidated Statements of Operations -- 13 weeks          3
                  ended April 29, 1998 and April 30, 1997

                  Consolidated Balance Sheets--                              4
                  April 29, 1998, April 30, 1997 and
                  January 28, 1998

                  Consolidated Statements of Cash Flows --                   5
                  13 weeks ended April 29, 1998 and
                  April 30, 1997

                  Notes to Consolidated Financial                            6
                  Statements

Item 2.           Management's Discussion and Analysis of Results of       7 - 8
                  Operations and Financial
                  Condition

PART II           OTHER INFORMATION

Item 6.           Exhibits and Reports on Form 8-K                           9

                  Signatures                                                10


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<PAGE>   3


PART I. FINANCIAL INFORMATION
ITEM 1. FINANCIAL STATEMENTS:

                                KMART CORPORATION
                      CONSOLIDATED STATEMENTS OF OPERATIONS
                  (DOLLARS IN MILLIONS, EXCEPT PER SHARE DATA)
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                                          13 WEEKS ENDED
                                                                       ---------------------
                                                                       APRIL 29,   APRIL 30,
                                                                          1998       1997
                                                                       ---------   ---------
<S>                                                                    <C>         <C>
Sales                                                                  $ 7,515     $ 7,263
Cost of sales, buying and occupancy                                      5,908       5,637
                                                                       -------     -------
Gross margin                                                             1,607       1,626
Selling, general and administrative expenses                             1,449       1,491
                                                                       -------     -------
Income before interest, income taxes and dividends on
     convertible preferred securities of subsidiary                        158         135
Interest expense, net                                                       74          98
Income tax provision                                                        24          11
Dividends on convertible preferred securities of subsidiary, net of
    income taxes of $7 and $6                                               13          12
                                                                       -------     -------
Net income                                                             $    47     $    14
                                                                       =======     =======


Basic income per common share                                          $  0.10     $  0.03
                                                                       =======     =======

Basic weighted average shares (millions)                                 489.7       485.3
</TABLE>







          See accompanying Notes to Consolidated Financial Statements.




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<PAGE>   4


                                KMART CORPORATION
                           CONSOLIDATED BALANCE SHEETS
                              (DOLLARS IN MILLIONS)
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                            APRIL 29,   APRIL 30,  JANUARY 28,
                                                                              1998        1997        1998
                                                                           ----------  ----------  -----------  
<S>                                                                        <C>         <C>         <C>    
Current Assets:
    Cash and equivalents                                                   $   733     $   316     $   498
    Merchandise inventories                                                  6,884       7,263       6,367
    Other current assets                                                       643         903         611
                                                                           -------     -------     -------
Total current assets                                                         8,260       8,482       7,476

Property and equipment, net                                                  5,558       5,667       5,472
Property held for sale or financing                                            120         200         271
Other assets and deferred charges                                              313         490         339
                                                                           -------     -------     -------
Total Assets                                                               $14,251     $14,839     $13,558
                                                                           =======     =======     =======

Current Liabilities:
   Long-term debt due within one year                                      $    77     $   104     $    78
   Trade accounts payable                                                    2,589       2,897       1,923
   Accrued payroll and other liabilities                                     1,034       1,212       1,064
   Taxes other than income taxes                                               227         232         209
                                                                           -------     -------     -------
Total current liabilities                                                    3,927       4,445       3,274

Long-term debt and notes payable                                             1,696       1,839       1,725
Capital lease obligations                                                    1,158       1,450       1,179
Other long-term liabilities                                                    968         960         965
Company obligated mandatorily redeemable convertible preferred
    securities of a subsidiary Trust holding solely 7 3/4% convertible
    junior subordinated debentures of Kmart (redemption value
    $1,000 at April 29, 1998)                                                  982         980         981
Common stock, 1,500,000,000 shares authorized; shares issued
     492,104,491, 487,849,549; and 488,811,271, respectively                   492         488         489
Capital in excess of par value                                               1,641       1,588       1,605
Retained earnings                                                            3,387       3,089       3,340
                                                                           -------     -------     -------
Total Liabilities and Shareholders' Equity                                 $14,251     $14,839     $13,558
                                                                           =======     =======     =======
</TABLE>






          See accompanying Notes to Consolidated Financial Statements.


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                                KMART CORPORATION
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                              (DOLLARS IN MILLIONS)
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                      13 WEEKS ENDED
                                                                    --------------------
                                                                    APRIL 29,  APRIL 30,
                                                                      1998      1997
                                                                    ---------  ---------   
<S>                                                                  <C>        <C>  
CASH FLOW FROM OPERATING ACTIVITIES:
     Net income from operations                                      $  47      $  14
     Adjustments to reconcile net income to net cash
          provided by operating activities:
          Depreciation and amortization                                165        170
          Increase in inventories                                     (517)      (909)
          Increase in accounts payable                                 666        888
          Changes in certain assets, liabilities and other items       (49)        41
                                                                     -----      -----
     Net cash provided by operating activities                         312        204
                                                                     -----      -----

CASH FLOW FROM INVESTING ACTIVITIES:
     Proceeds from sale of assets and divestiture                      109        113
     Capital expenditures                                             (145)      (128)
     Decrease (increase) in property held for resale                   (24)        88
     Other - net                                                        (5)       (27)
                                                                     -----      -----
     Net cash provided (used) by investing activities                  (65)        46
                                                                     -----      -----

CASH FLOW FROM FINANCING ACTIVITIES:
     Changes in common stock                                            39         19
     Proceeds from issuance of long-term debt and notes payable          -        335
     Reduction in capital lease obligations                            (21)       (26)
     Reduction in long-term debt and notes payable                     (30)      (668)
                                                                     -----      -----
     Net cash used for financing activities                            (12)      (340)
                                                                     -----      -----

Net increase (decrease) in cash and equivalents                        235        (90)
Cash and equivalents at beginning of year                              498        406
                                                                     -----      -----
Cash and equivalents at end of period                                $ 733      $ 316
                                                                     =====      =====
</TABLE>









          See accompanying Notes to Consolidated Financial Statements.



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<PAGE>   6


                                KMART CORPORATION
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                   (UNAUDITED)

1.)  BASIS OF PRESENTATION

         These interim unaudited consolidated financial statements have been
prepared in accordance with the rules and regulations of the Securities and
Exchange Commission, and, in the opinion of management, reflect all adjustments
(which include normal recurring adjustments) necessary for a fair statement of
the results for the interim periods. These consolidated financial statements
should be read in conjunction with the financial statements and the notes
thereto included in the Company's 1997 Annual Report and Form 10-K filed for the
fiscal year ended January 28, 1998.

         Certain reclassifications of the January 28, 1998 and April 30, 1997
consolidated balance sheet and cash flows have been made to conform to current
year presentation.


2.)  DISCONTINUED OPERATIONS AND DIVESTITURES

         In February 1998, the Company's minority interest in Kmart Canada Co.
was purchased by Hudson's Bay Co. Under the terms of the purchase, Kmart
received approximately $8 million for its remaining equity interest in Kmart
Canada Co., along with $79 million for repayment of its note and debentures.


3.)  INVENTORIES AND COST OF MERCHANDISE SOLD

         A substantial portion of the Company's inventory is accounted for using
the last-in, first-out (LIFO) method. Since LIFO costs can only be determined at
the end of each fiscal year when inflation rates and inventory levels are
finalized, estimates are used for LIFO purposes in the interim consolidated
financial statements. Inventories valued on LIFO at April 29, 1998, April 30,
1997 and January 28, 1998 were $457 million, $445 million and $457 million lower
than the amounts that would have been reported under the first-in, first-out
(FIFO) method, respectively.


4.)  SUBSEQUENT EVENT

         On May 1, 1998, the Company entered into an agreement with Kimco Realty
Corporation to lease approximately 50 stores currently operated by Venture 
Stores, Inc. These stores will be converted to the Big Kmart format and
are scheduled to be operational in the fourth quarter of 1998.




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<PAGE>   7



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

RESULTS OF OPERATIONS

<TABLE>
<CAPTION>
                                                                           % CHANGE
                                                                 ------------------------------
     ($ Millions)                     APRIL 29,   APRIL 30,                         COMPARABLE 
                                        1998        1997         ALL STORES           STORES
                                      ---------   ---------      ----------         -----------
SALES
<S>                                   <C>         <C>                <C>                 <C>
     General Merchandise
         United States                $   7,515   $   7,061          6.4                 6.1
         International                      -           202       (100.0)                  -
                                      ---------   ---------
     Consolidated Sales               $   7,515   $   7,263          3.5                 6.1
                                      =========   =========

OPERATING INCOME
     United States                    $     158   $     139                   
     International                          -            (4)                 
                                      ---------   ---------
     Consolidated Operating Income    $     158   $     135                  
                                      =========   =========
</TABLE>

         SALES and comparable store sales increased 3.5% and 6.1%, respectively
for the 13 weeks ended April 29, 1998. The increases were primarily due to:
improved merchandise assortments; continued roll out of the Big Kmart format,
with 118 store conversions during the quarter; and execution of the Company's
competitive pricing strategy. Divisions showing particular strength for the
quarter included apparel, consumables, home electronics and appliances,
pharmacy, home fashions and jewelry. The Company operated a total of 2,118
stores as of April 29, 1998 compared to 2,245 stores for the same period of the
prior year and closed 18 stores during the first quarter.


         GROSS MARGIN, as a percentage of sales, was 21.4% and 22.4% for the 13
weeks ended April 29, 1998 and April 30, 1997, respectively. The decline in the
percentage reflects the execution of the Company's competitive pricing strategy,
growth in consumable sales and faster in-season clearance of apparel inventory.


         SELLING, GENERAL AND ADMINISTRATIVE ("SG&A") EXPENSES, as a percentage
of sales, were 19.3% and 20.5%, for the 13 weeks ended April 29, 1998, and April
30, 1997, respectively. The 1.2 percentage point reduction, or $42 million,
resulted primarily from the sale of international operations and increased
leverage given additional sales volumes.


         OPERATING INCOME for the 13 weeks ended April 29, 1998 was $158
million, or 2.1% of sales, as compared to operating income of $135 million, or
1.9% of sales, for the same period of the prior year. This increase was the
result of increased sales volumes, continued leveraging of SG&A expenses and the
sale of the remaining interest in Kmart Canada Co.


         NET INTEREST EXPENSE for the 13 weeks ended April 29, 1998 was $74
million as compared to $98 million for the same period of the prior year. Net
interest expense decreased as a result of lower levels of borrowings, primarily
attributable to the payoff of the revolver and the term loan. See "Liquidity and
Financial Condition".




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<PAGE>   8



                                KMART CORPORATION
        MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF OPERATIONS AND
                        FINANCIAL CONDITION -- CONTINUED


LIQUIDITY AND FINANCIAL CONDITION

         Kmart's primary sources of working capital are cash flows from
operations and borrowings under its credit facilities. The Company had working
capital of $4,333, $4,037 and $4,202 million at April 29, 1998, April 30, 1997,
and January 28, 1998, respectively. The Company's working capital fluctuates in
relation to profitability, seasonal inventory levels net of trade accounts
payable and the level of store openings and closings.

         In March, 1998, the collateral securing the Company's borrowings under
the Revolving Credit Agreement was released. The Company continued to be in
compliance with all covenants contained in the Agreement during the first
quarter of 1998.

         Net cash provided by operating activities for the 13 weeks ended April
29, 1998 was $312 million as compared to $204 million for the same period in
1997. The increase in cash was primarily the result of increased earnings and
the reduction in cash used for net inventory.

         Net cash used for investing activities was $65 million for the 13 weeks
ended April 29, 1998 compared to net cash provided by investing activities of
$46 million for the same period in 1997. The decrease in cash provided by
investing activities was primarily the result of lower levels of sale-leaseback
transactions in the current year.

         Net cash used for financing activities was $12 million for the 13 weeks
ended April 29, 1998 compared to $340 million for the same period in 1997. Cash
used for financing during 1997 was the result of paying down the Company's
remaining balance on the Term Loan as well as payments on certain mortgages and
medium term notes. These amounts were partially offset by the issuance of $335
million in Commercial Mortgage Pass Through Securities.

         Management believes the funds generated by operations, together with
funds available under existing credit arrangements, are sufficient to meet the
Company's currently anticipated funding requirements.


OTHER MATTERS

         The Company continues to work to resolve the potential impact of the
Year 2000 on the processing of date-sensitive information by the Company's
computerized information systems. Total costs of modifying the Company's current
systems are estimated at $50 million and are not expected to have a material
adverse impact on the Company's financial position, results of operations or
cash flows in future periods. However, if the Company or its vendors are unable
to resolve such processing issues in a timely manner, a material financial risk
could result.

         Effective April 3, 1998, the American Institute of Certified Public
Accountants' Accounting Standards Executive Committee issued Statement of
Position ("SOP") No. 98-5, "Reporting on the Costs of Start-Up Activities",
which requires that pre-opening costs and related organization costs be expensed
as incurred. This statement does not have a material effect on the Company's
financial position or results of operations.

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<PAGE>   9




PART II. OTHER INFORMATION



ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

(a)      The following exhibits are filed as a part of this report:

         Exhibit 11 - Information on Computation of Per Share Earnings
         Exhibit 27 - Financial Data Schedule

(b)      Reports on Form 8-K: No reports were filed on Form 8-K by the
         Registrant during the 13 weeks ended April 29, 1998.







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                                   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.

The signatory hereby acknowledges and adopts the typed form of his name in the
electronic filing of this document with the Securities and Exchange Commission.





                                       Date:             June 11, 1998
                                                       Kmart Corporation
                                               -----------------------------
                                                         (Registrant)


                                        By:             M.E. Welch, III
                                               -----------------------------
                                                        M.E. Welch, III
                                                   SENIOR VICE PRESIDENT AND
                                                    CHIEF FINANCIAL OFFICER
                                                   (Duly Authorized Officer,
                                                 Principal Financial Officer)

                                        By:         William C. Najdecki
                                               -----------------------------
                                                    William C. Najdecki
                                                  VICE PRESIDENT, CONTROLLER
                                                   (Duly Authorized Officer,
                                                 Principal Accounting Officer)





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