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

                                    FORM 10-Q


         (MARK ONE)

          X  QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES
        ---- EXCHANGE ACT OF 1934 FOR THE QUARTERLY PERIOD ENDED MAY 2, 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 NUMBER 1-12814

                            COLE NATIONAL CORPORATION
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)


           DELAWARE                                      34-1453189
     (STATE OR OTHER JURISDICTION OF                   (I.R.S. EMPLOYER
     INCORPORATION OR ORGANIZATION)                   IDENTIFICATION NO.)


           5915 LANDERBROOK DRIVE
           MAYFIELD HEIGHTS, OHIO                          44124
     (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)            (ZIP CODE)

                                 (440) 449-4100
              (REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE)



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.                    X  YES      NO
                                                     ---       ---

AS OF MAY 29, 1998, 14,899,415 SHARES OF THE REGISTRANT'S COMMON STOCK WERE
OUTSTANDING.

================================================================================

<PAGE>   2

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                   COLE NATIONAL CORPORATION AND SUBSIDIARIES
                                    FORM 10-Q
                            QUARTER ENDED MAY 2, 1998
                                      INDEX

<TABLE>
<CAPTION>
                                                                                             PAGE NO.

PART I.  FINANCIAL INFORMATION

         ITEM 1.  FINANCIAL STATEMENTS

<S>                                                                                             <C> 
                  CONSOLIDATED BALANCE SHEETS AS OF MAY 2, 1998 AND JANUARY 31,
                  1998......................................................................      1

                  CONSOLIDATED STATEMENTS OF OPERATIONS FOR THE 13 WEEKS ENDED MAY 2,
                  1998 AND MAY 3, 1997......................................................      2

                  CONSOLIDATED STATEMENTS OF CASH FLOWS FOR THE 13 WEEKS ENDED MAY 2,
                  1998 AND MAY 3, 1997......................................................      3

                  NOTES TO CONSOLIDATED FINANCIAL STATEMENTS................................      4

         ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
                  RESULTS OF OPERATIONS.....................................................    6 - 8

PART II. OTHER INFORMATION

         ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K..........................................      9
</TABLE>





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<PAGE>   3


                         PART I - FINANCIAL INFORMATION
ITEM 1.  FINANCIAL STATEMENTS
                   COLE NATIONAL CORPORATION AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEETS
                                   (UNAUDITED)
                             (DOLLARS IN THOUSANDS)
<TABLE>
<CAPTION>
                                                                          May 2,       January 31,
                                                                           1998            1998
                                                                       -----------     -----------
<S>                                                                 <C>             <C>        
Assets
------
Current assets:
    Cash and temporary cash investments                             $    37,707     $    68,053
    Accounts receivable, less allowance for doubtful accounts of
       $7,039 in 1998 and $4,334 in 1997                                 56,060          52,030
    Current portion of notes receivable                                   4,293           4,177
    Refundable income taxes                                               9,520           9,520
    Inventories                                                         121,570         119,970
    Prepaid expenses and other                                            6,875           9,195
    Deferred income tax benefits                                         21,534          21,534
                                                                    -----------     -----------
          Total current assets                                          257,559         284,479

Property and equipment, at cost                                         248,440         242,966
    Less-accumulated depreciation and amortization                     (121,296)       (115,162)
                                                                    -----------     -----------
          Total property and equipment, net                             127,144         127,804
Other assets:
    Notes receivable, excluding current portion                          36,963          25,783
    Deferred income taxes and other                                      59,652          54,241
    Intangible assets, net                                              158,239         159,077
                                                                    -----------     -----------
          Total assets                                              $   639,557     $   651,384
                                                                    ===========     ===========
Liabilities and Stockholders' Equity
------------------------------------
Current liabilities:
    Current portion of long-term debt                               $    16,051     $    16,027
    Accounts payable                                                     49,186          71,867
    Accrued interest                                                      7,435           6,615
    Net liabilities of discontinued operations                            4,544           3,475
    Accrued liabilities                                                 110,739         112,363
    Accrued income taxes                                                  4,421             957
                                                                    -----------     -----------
          Total current liabilities                                     192,376         211,304

Long-term debt, net of discount and current portion                     277,060         277,401

Other long-term liabilities                                              30,654          30,664
Stockholders' equity:
    Preferred stock                                                           -               -
    Common stock                                                             15              15
    Paid-in capital                                                     252,480         251,405
    Foreign currency translation adjustment                              (1,484)         (1,749)
    Notes receivable - stock option exercise                               (926)           (926)
    Accumulated deficit                                                (110,007)       (116,119)
    Treasury stock at cost                                                 (611)           (611)
                                                                    -----------     -----------
          Total stockholders' equity                                    139,467         132,015
                                                                    -----------     -----------
          Total liabilities and stockholders' equity
                                                                    $   639,557     $   651,384
                                                                    ===========     ===========
</TABLE>

The accompanying notes to consolidated financial statements are an integral part
of these consolidated balance sheets.


                                      -1-
<PAGE>   4

                   COLE NATIONAL CORPORATION AND SUBSIDIARIES
                      CONSOLIDATED STATEMENTS OF OPERATIONS
                                   (UNAUDITED)
                (DOLLARS IN THOUSANDS, EXCEPT PER SHARE AMOUNTS)

<TABLE>
<CAPTION>
                                                                     13 Weeks Ended
                                                                ------------------------
                                                                   May 2,        May 3,
                                                                   1998          1997
                                                                ----------    ----------

<S>                                                             <C>           <C>       
Net revenue                                                     $  271,828    $  239,686

Costs and expenses:
    Cost of goods sold                                              90,289        82,412
    Operating expenses                                             156,318       136,041
    Depreciation and amortization                                    8,398         7,460
                                                                ----------    ----------
       Total costs and expenses                                    255,005       225,913
                                                                ----------    ----------

Income from continuing operations                                   16,823        13,773

Interest expense, net                                                6,287         7,783
                                                                ----------    ----------

Income from continuing operations before income taxes               10,536         5,990

Income tax provision                                                 4,424         2,636
                                                                ----------    ----------

Income from continuing operations                                    6,112         3,354

Operating loss from discontinued operations,
    net of income taxes                                                  -          (906)
                                                                ----------    ----------

Net income                                                      $    6,112    $    2,448
                                                                ==========    ==========



Earnings (loss) per common share:
    Basic-
       Income from continuing operations                        $      .41    $      .28
       Loss from discontinued operations                                 -          (.08)
                                                                ----------    ----------
       Net income                                               $      .41    $      .20
                                                                ==========    ==========

    Diluted-
       Income from continuing operations                        $      .40    $      .27
       Loss from discontinued operations                                 -          (.07)
                                                                ----------    ----------
       Net income                                               $      .40    $      .20
                                                                ==========    ==========
</TABLE>






The accompanying notes to consolidated financial statements are an integral part
of these consolidated statements.


                                      -2-
<PAGE>   5

                   COLE NATIONAL CORPORATION AND SUBSIDIARIES
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)
                             (DOLLARS IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                                                13 Weeks Ended
                                                                                            ---------------------
                                                                                              May 2,      May 3,
                                                                                              1998         1997
                                                                                            --------     --------
<S>                                                                                         <C>          <C>     
Cash flows from operating activities:
    Net income                                                                              $  6,112     $  2,448
    Adjustments to reconcile net income to net cash used by
       operating activities:
          Depreciation and amortization                                                        8,398        7,460
          Non-cash interest                                                                     (226)          96
          Change in assets and liabilities:
             Decrease (increase) in accounts and notes 
               receivable, prepaid expenses and other assets                                  (1,957)         630
             Decrease (increase) in net assets of discontinued 
               operations                                                                      1,069       (1,864)
             Increase in inventories                                                          (1,502)      (7,864)
             Decrease in accounts payable, accrued liabilities 
               and other liabilities                                                         (23,755)     (23,791)
             Increase (decrease) in accrued interest                                             820         (924)
             Increase (decrease) in accrued income taxes                                       3,464      (15,877)
                                                                                            --------     --------
                 Net cash used by operating activities                                        (7,577)     (39,686)
                                                                                            --------     --------

Cash flows from investing activities:
    Purchases of property and equipment, net                                                  (5,973)     (11,187)
    Systems development costs                                                                 (6,332)      (2,078)
    Investment in Pearle Europe                                                              (10,296)           -
    Other, net                                                                                  (678)        (378)
                                                                                            --------     --------
                 Net cash used by investing activities                                       (23,279)     (13,643)
                                                                                            --------     --------

Cash flows from financing activities:
    Repayment of long-term debt                                                                 (335)        (296)
    Net proceeds from exercise of stock options and warrants                                     818          841
    Other, net                                                                                    27         (152)
                                                                                            --------     --------
                 Net cash provided by financing activities                                       510          393
                                                                                            --------     --------

Cash and temporary cash investments:
  Net decrease during the period                                                             (30,346)     (52,936)
  Balance, beginning of the period                                                            68,053       73,141
                                                                                            --------     --------
  Balance, end of the period                                                                $ 37,707     $ 20,205
                                                                                            ========     ========
</TABLE>


The accompanying notes to consolidated financial statements are an integral part
of these consolidated statements.

                                      -3-
<PAGE>   6

                   COLE NATIONAL CORPORATION AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                   (UNAUDITED)

     (1)  BASIS OF PRESENTATION AND ACCOUNTING POLICIES

          The consolidated financial statements include the accounts of Cole
     National Corporation (CNC), its wholly owned subsidiaries, including Cole
     National Group, Inc. (CNG), and CNG's wholly owned subsidiaries
     (collectively, the "Company"). All significant intercompany transactions
     have been eliminated in consolidation.

          The accompanying consolidated financial statements have been prepared
     without audit and certain information and footnote disclosures normally
     included in financial statements prepared in accordance with generally
     accepted accounting principles have been condensed or omitted, although the
     Company believes that the disclosures herein are adequate to make the
     information not misleading. Results for interim periods are not necessarily
     indicative of the results to be expected for the full year. These
     statements should be read in conjunction with the Company's consolidated
     financial statements for the fiscal year ended January 31, 1998.

          In the opinion of management, the accompanying financial statements
     contain all adjustments (consisting only of normal recurring accruals)
     necessary to present fairly the Company's financial position as of May 2,
     1998 and the results of operations and cash flows for the 13 weeks ended
     May 2, 1998 and May 3, 1997.

          Inventories

          The accompanying interim consolidated financial statements have been
     prepared without physical inventories.

           Cash Flows

          Net cash flows from operating activities reflect cash payments for
     income taxes and interest of $443,000 and $5,838,000, respectively, for the
     13 weeks ended May 2, 1998, and $17,967,000 and $9,553,000, respectively,
     for the 13 weeks ended May 3, 1997.

          Earnings Per Share

          Earnings per share for the 13 weeks ended May 2, 1998 and May 3, 1997
     have been calculated based on the following weighted average number of
     common shares and equivalents, if applicable, outstanding:

<TABLE>
<CAPTION>
                                           1998                    1997
                                      -------------             -----------

<S>                                    <C>                      <C>       
                  Basic                14,754,887               12,019,488
                  Diluted              15,277,070               12,481,113
</TABLE>



                                      -4-
<PAGE>   7

     (2)  INVESTMENT IN PEARLE EUROPE B.V.

          In February 1998, the Company repaid a $3.2 million note payable to a
     subsidiary of Pearle Europe and invested an additional $7.2 million in the
     form of 8% shareholder loans to Pearle Europe in connection with Pearle
     Europe's acquisition of optical operations in Germany and Austria.

     (3)  NEW ACCOUNTING PRONOUNCEMENT

          Effective February 1, 1998, the Company adopted Statement of Financial
     Accounting Standards (SFAS) No. 130, "Reporting Comprehensive Income". This
     statement requires that the Company report the change in its equity during
     a period from non-owner sources. For the 13 weeks ended May 2, 1998 and May
     3, 1997, components of other comprehensive income (loss) relate to foreign
     currency translation adjustments related to the Company's Canadian
     operations and investment in Pearle Europe B.V. Total comprehensive income
     is as follows (000's omitted):

<TABLE>
<CAPTION>
                                                          13 Weeks Ended
                                                  ------------------------------
                                                   May 2, 1998      May 3, 1997
                                                  ------------      ------------

<S>                                               <C>               <C>         
Net income                                        $      6,112      $      2,448
Other comprehensive income (loss)                          265              (46)
                                                  ------------      ------------
Total comprehensive income                        $      6,377      $      1,988
                                                  ============      ============
</TABLE>

     (4)  RECLASSIFICATIONS

          Certain 1997 amounts have been reclassified to conform with the 1998
     presentation.


                                      -5-
<PAGE>   8

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

          The following is a discussion of certain factors affecting the
     Company's results of operations for the 13 week periods ended May 2, 1998
     and May 3, 1997 (the Company's first quarter) and its liquidity and capital
     resources. This discussion should be read in conjunction with the
     consolidated financial statements and notes thereto included elsewhere in
     this filing and the Company's audited financial statements for the fiscal
     year ended January 31, 1998 included in its annual report on Form 10-K.

          The Company's fiscal year ends on the Saturday closest to January 31.
     Fiscal years are identified according to the calendar year in which they
     begin. For example, the fiscal year ended January 31, 1998 is referred to
     as "fiscal 1997."

     RESULTS OF OPERATIONS

          Net revenue for the first quarter of fiscal 1998 increased 13.4% to
     $271.8 million from $239.7 million for the same period in fiscal 1997. The
     increase was primarily attributable to the opening of additional Cole
     Optical units including the American Vision Centers, Inc. ("AVC") stores
     acquired in August 1997, a consolidated comparable store sales increase of
     3.7% and the growth of managed vision care fees. At Cole Optical,
     comparable store sales increased 4.6% and 1.7% at Cole Vision and Pearle,
     respectively. The Pearle increase was impacted by a weaker than expected
     reception to a new promotional offer in February and March. At Things
     Remembered, the comparable store sales increase of 4.6% reflected increased
     sales of additional personalization, new products and clearance
     merchandise. At May 2, 1998, the Company had 2,832 specialty service retail
     locations, including 401 franchised locations, compared to 2,664 at May 3,
     1997.

          Gross profit increased 15.4% to $181.5 million in the first quarter of
     fiscal 1998 from $157.3 million in the same period last year. The gross
     profit increase was primarily attributable to the increased revenue at Cole
     Optical and Things Remembered. Gross margins for the first quarter of
     fiscal 1998 and fiscal 1997 were 66.8% and 65.6%, respectively. Gross
     margin was favorably impacted by the growth in managed vision care fees and
     the sales mix of higher margin products at Cole Optical.

          Operating expenses increased 14.9% to $156.3 million in the first
     quarter of fiscal 1998 from $136.0 million in fiscal 1997, and as a
     percentage of revenue, operating expenses increased to 57.5% in fiscal 1998
     from 56.8% in fiscal 1997. The leverage loss was primarily a result of
     increased advertising expenditures at Pearle and increased expenses related
     to managed vision care fee growth partially offset by leverage gains on
     payroll and store occupancy costs. Fiscal 1998 depreciation and
     amortization expense of $8.4 million was $0.9 million more than fiscal 1997
     reflecting the acquisition of AVC and an increase in capital expenditures.

          Income from operations increased 22.1% to $16.8 million for the first
     quarter of fiscal 1998 from $13.8 million for the same period a year ago,
     primarily the result of the increase in net revenue, partially offset by
     leverage loss from additional advertising expenditures.


                                      -6-
<PAGE>   9

          Net interest expense decreased $1.5 million from the first quarter of
     fiscal 1997 to $6.3 million in the first quarter of fiscal 1998. The
     decrease was primarily attributable to the purchase and retirement of
     $150.9 million of 11-1/4% Senior Notes in conjunction with a tender offer
     in September 1997 partially offset by additional interest on $125.0 million
     of 8-5/8% Senior Subordinated Notes issued in August 1997.

          An income tax provision was recorded in the first quarter of fiscal
     1998 and fiscal 1997 using the Company's estimated annual effective tax
     rate of 42% and 44%, respectively. The reduction in the rate primarily
     reflects the estimated impact of non-deductible amortization of goodwill in
     both years.

          Net income increased to $6.1 million for the first quarter of fiscal
     1998 from $2.4 million for the first quarter of fiscal 1997. The increase
     was due to improvement in income from continuing operations, the reduction
     of net interest expense and a $0.9 million loss from discontinued
     operations in the first quarter of fiscal 1997.

     LIQUIDITY AND CAPITAL RESOURCES

          The Company's primary source of liquidity is funds provided from
     operations of its operating subsidiaries. In addition, the Company's
     operating subsidiaries have available to them working capital commitments
     of $75.0 million under their Credit Facility, reduced by commitments under
     letters of credit. There were no working capital borrowings outstanding
     during the first quarter of fiscal 1998 and fiscal 1997.

          Operations for the first quarter used $7.6 million of cash in fiscal
     1998 compared to $39.7 million in fiscal 1997. The decrease in cash used by
     operations was primarily attributable to the payment in 1997 of $15.0
     million of taxes due on the sale of Pearle's European operation, a smaller
     increase in first quarter inventories in 1998 and the increase in net
     income.

          Cash used by investing activities included capital additions of $6.0
     million and $11.2 million for the first quarter of fiscal 1998 and fiscal
     1997, respectively. The majority of capital expenditures were for store
     fixtures, equipment and leasehold improvements for new stores and the
     remodeling of existing stores. In fiscal 1997, capital expenditures of $4.4
     million were incurred in connection with the construction of Things
     Remembered's new warehouse and distribution facility. In May 1998, the
     Company purchased an office building in Twinsburg, Ohio for $9.5 million.
     It is anticipated that a portion of Cole Optical's business will move there
     during 1998. The Company is currently evaluating financing alternatives for
     both facilities. In February 1998, the Company repaid a $3.2 million note
     payable to a subsidiary of Pearle Europe B.V. (Pearle Europe) and invested
     an additional $7.2 million in the form of 8% shareholder loans to Pearle
     Europe in connection with Pearle Europe's acquisition of two optical
     operations in Germany and Austria. Investments in systems development costs
     totaled $6.3 and $2.1 million in the first quarter of fiscal 1998 and
     fiscal 1997, respectively.

          The Company believes that funds provided from operations along with
     funds available under the Credit Facility will provide adequate sources of
     liquidity to allow the Company's operating subsidiaries to continue to
     expand the number of stores and to fund capital expenditures and systems
     development costs.

                                      -7-
<PAGE>   10

     FORWARD-LOOKING INFORMATION

          Certain sections of this Form 10-Q contain forward-looking statements.
     Forward-looking statements are made based upon management's expectations
     and beliefs concerning future events impacting the Company. All
     forward-looking statements involve risk and uncertainty.

          The Company operates in a highly competitive environment, and its
     future liquidity, financial condition and operating results may be
     materially affected by a variety of factors, some of which may be beyond
     the control of the Company, including risks associated with the integration
     of acquired operations, the Company's ability to select and stock
     merchandise attractive to customers, the implementation of its store
     acquisition program, the ability to attract Managed Vision Care accounts,
     economic and weather factors affecting consumer spending, operating
     factors, including manufacturing quality of optical and engraved goods,
     affecting customer satisfaction, the Company's relationships with host
     stores, franchisees and Managed Vision Care customers, the mix of goods
     sold, pricing and other competitive factors and the seasonality of the
     Company's business.


                                      -8-
<PAGE>   11

                           PART II - OTHER INFORMATION


     ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K

     (a)  Exhibits. The following Exhibits are filed herewith and made a part
          hereof:

          27        Financial Data Schedule

          10.1      Third Amendment to the Credit Agreement, dated as of May 15,
                    1998, among Cole Vision Corporation, Things Remembered,
                    Inc., Pearle, Inc., and Pearle Service Corporation and
                    Canadian Imperial Bank of Commerce.

     (b)  Reports on Form 8-K

          The Company has not filed any reports on Form 8-K for the quarterly
          period ended May 2, 1998.


                                      -9-
<PAGE>   12

                                    SIGNATURE
                                    ---------

         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.


                               COLE NATIONAL CORPORATION



                               By:      /s/ Wayne L. Mosley
                                    --------------------------------------
                                    Wayne L. Mosley
                                    Vice President and Controller
                                    (Duly Authorized Officer and Principal
                                    Accounting Officer)

                             Date:  June 9, 1998



                                      -10-
<PAGE>   13

                            COLE NATIONAL CORPORATION
                                    FORM 10-Q
                            QUARTER ENDED MAY 2, 1998

                                  EXHIBIT INDEX


       Exhibit
       Number       Description
       --------     -----------

          27        Financial Data Schedule

          10.1      Third Amendment to the Credit Agreement, dated as of May 15,
                    1998, among Cole Vision Corporation, Things Remembered,
                    Inc., Pearle, Inc., and Pearle Service Corporation and
                    Canadian Imperial Bank of Commerce.









                                      -11-