<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 33-66342

                            COLE NATIONAL GROUP, INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)


             DELAWARE                                        34-1744334
(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)

THE REGISTRANT MEETS THE CONDITIONS SET FORTH IN GENERAL INSTRUCTION H(1)(a) AND
(b) OF FORM 10-Q AND IS THEREFORE FILING THIS FORM IN THE REDUCED DISCLOSURE
FORMAT.

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
                                       ---     ---

ALL OF THE OUTSTANDING CAPITAL STOCK OF THE REGISTRANT IS HELD BY COLE NATIONAL
CORPORATION.

AS OF MAY 28, 1998, 1,100 SHARES OF THE REGISTRANT'S COMMON STOCK, $.01 PAR
VALUE, WERE OUTSTANDING.

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

<PAGE>   2


                   COLE NATIONAL GROUP, INC. AND SUBSIDIARIES
                                    FORM 10-Q
                            QUARTER ENDED MAY 2, 1998
                                      INDEX

                                                                        PAGE NO.
<TABLE>

<S>      <C>                                                                                          <C>
PART I.  FINANCIAL INFORMATION

         ITEM 1.  FINANCIAL STATEMENTS

                  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 - 7

PART II. OTHER INFORMATION

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




<PAGE>   3
                         PART I - FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS

                   COLE NATIONAL GROUP, INC. AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEETS
                                   (UNAUDITED)
                             (DOLLARS IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                May 2,        January 31,
Assets                                                          1998              1998
------                                                       --------            ------
<S>                                                         <C>               <C>      
Current assets:
    Cash and temporary cash investments                     $  37,707         $  67,989
    Accounts receivable, less allowance for doubtful
       accounts of $7,039 in 1998 and $4,334 in 1997           55,446            51,491
    Current portion of notes receivable                         4,293             4,177
    Inventories                                               121,570           119,970
    Prepaid expenses and other                                  6,805             9,099
    Deferred income tax benefits                               20,950            20,950
                                                            ---------         ---------
          Total current assets                                246,771           273,676

Property and equipment, at cost                               243,086           237,611
    Less - accumulated depreciation and amortization         (119,854)         (113,954)
                                                            ---------         ---------
          Total property and equipment, net                   123,232           123,657

Other assets:
    Notes receivable, excluding current portion                19,755            19,552
    Deferred income taxes and other                            57,515            52,373
    Intangible assets, net                                    158,239           159,077
                                                            ---------         ---------
          Total assets                                      $ 605,512         $ 628,335
                                                            =========         =========

Liabilities and Stockholder's Equity
------------------------------------
Current liabilities:
    Current portion of long-term debt                       $  15,086         $  15,078
    Accounts payable                                           48,666            71,672
    Payable to affiliates                                      79,449            88,776
    Accrued interest                                            7,435             6,615
    Net liabilities of discontinued operations                  4,544             3,475
    Accrued liabilities                                       107,100           108,545
    Accrued income taxes                                        4,239               965
                                                            ---------         ---------
          Total current liabilities                           266,519           295,126

Long-term debt, net of discount and current portion           274,898           274,992

Other long-term liabilities                                    30,654            30,664

Stockholder's equity:
    Common stock                                                  -                 -
    Paid-in capital                                           193,560           193,560
    Foreign currency translation adjustment                      (407)             (436)
    Accumulated deficit                                      (159,712)         (165,571)
                                                            ---------         ---------
          Total stockholder's equity                           33,441            27,553
                                                            ---------         ---------
          Total liabilities and stockholder's equity        $ 605,512         $ 628,335
                                                            =========         =========
</TABLE>

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

                                      -1-
<PAGE>   4
                   COLE NATIONAL GROUP, INC. AND SUBSIDIARIES
                      CONSOLIDATED STATEMENT OF OPERATIONS
                                   (UNAUDITED)
                             (DOLLARS IN THOUSANDS)

<TABLE>
<CAPTION>

                                                                   13 Weeks Ended
                                                             ---------------------------
                                                               May 2,           May 3,
                                                                1998             1997
                                                             ---------        ---------

<S>                                                          <C>              <C>      
Net revenue                                                  $ 270,742        $ 238,698

Costs and expenses:
    Cost of goods sold                                          90,289           82,412
    Operating expenses                                         155,460          135,263
    Depreciation and amortization                                8,163            7,252
                                                             ---------        ---------
        Total costs and expenses                               253,912          224,927
                                                             ---------        ---------

Income from continuing operations                               16,830           13,771

Interest expense, net                                            6,730            7,865
                                                             ---------        ---------                                            
Income from continuing operations before income taxes           10,100            5,906

Income tax provision                                             4,241            2,599
                                                             ---------        ---------

Income from continuing operations                                5,859            3,307

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

Net income                                                   $   5,859        $   2,401
                                                             =========        =========
</TABLE>

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

                                      -2-
<PAGE>   5


                   COLE NATIONAL GROUP, INC. 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                                                               $  5,859         $  2,401
    Adjustments to reconcile net income to net cash used by operating
       activities:
         Depreciation and amortization                                          8,163            7,252
         Non-cash interest                                                        261              225
         Change in assets and liabilities:                                            
             Decrease (increase) in accounts and notes                                
                receivable, prepaid expenses and                                      
                other assets                                                   (1,908)             539
             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                             (24,204)         (24,319)
             Increase (decrease) in accrued interest                              820             (924)
             Increase (decrease) in accrued income taxes                        3,274             (921)
                                                                             --------         --------
                 Net cash used by operating activities                         (8,168)         (25,475)
                                                                             --------         --------

Cash flows from investing activities:
    Purchases of property and equipment, net                                   (5,973)         (11,180)
    Systems development costs                                                  (6,332)          (2,543)
    Other, net                                                                   (452)             116
                                                                             --------         --------
                 Net cash used by investing activities                        (12,757)         (13,607)
                                                                             --------         --------

Cash flows from financing activities:
    Repayment of long-term debt                                                  (104)             (85)
    Advances to affiliates, net                                                (9,281)         (13,617)
    Other, net                                                                     28              155)
                                                                             --------         --------
                 Net cash used by financing activities                         (9,357)         (13,857)
                                                                             --------         --------

Cash and temporary cash investments:
    Net decrease during the period                                            (30,282)         (52,939)
    Balance, beginning of the period                                           67,989           73,141
                                                                             --------         --------
    Balance, end of the period                                               $ 37,707         $ 20,202
                                                                             ========         ========
</TABLE>

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

                                      -3-

<PAGE>   6


                   COLE NATIONAL GROUP, INC. 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 Group, Inc. (CNG) and its wholly owned subsidiaries (collectively, the
Company). CNG is a wholly owned subsidiary of Cole National Corporation. 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 and notes
thereto included in the Company's annual report on Form 10-K 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 $450,000 and $5,780,000, respectively, for the 13 weeks
ended May 2, 1998, and $2,974,000 and $9,492,000, respectively, for the 13 weeks
ended May 3, 1997.

(2) 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. Total
comprehensive income is as follows (000's omitted):

                                      -4-

<PAGE>   7


<TABLE>
<CAPTION>

                                                              13 Weeks Ended
                                                     -----------------------------
                                                     May 2, 1998       May 3, 1997
                                                     -----------       -----------

<S>                                                    <C>              <C>              
       Net income                                      $ 5,859          $ 2,401
       Other comprehensive income (loss)                    29             (156)
                                                       -------          -------
       Total comprehensive income                      $ 5,888          $ 2,245
                                                       =======          =======
</TABLE>


(3)   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

         Certain information required by this item has been omitted pursuant to
General Instruction H of Form 10-Q.

         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). 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
$270.7 million from $238.7 million for the same period in fiscal 1997. The
increase was primarily attributable to the opening of additional Cole Optical
units including the 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 15.5% to $180.5 million in the first quarter of
fiscal 1998 from $156.3 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 66.7% and 65.5%, 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 $155.5 million in the first
quarter of fiscal 1998 from $135.3 million in fiscal 1997, and as a percentage
of revenue, operating expenses increased to 57.4% in fiscal 1998 from 56.7% 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 $8.2 million was $0.9
million more than fiscal 1997 reflecting the acquisition of AVC and an increase
in capital expenditures.

                                       -6-

<PAGE>   9



         Income from operations increased 22.2% 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 expense
leverage loss from additional advertising expenditures and managed vision care
expenses.

         Net interest expense decreased $1.1 million from the first quarter of
fiscal 1997 to $6.7 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 $5.9 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.

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.


                                      -7-
<PAGE>   10
                           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
           Commerce, incorporated by reference to Exhibit 10.1 of Cole
           National Corporation's Quarterly Report on Form 10-Q for the
           period ended May 2, 1998 (File 1-12814)

    (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.

                                      -8-
<PAGE>   11


                                    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 GROUP, INC.



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

                           Date:  June 9, 1998

                                      -9-

<PAGE>   12




                            COLE NATIONAL GROUP, INC.
                                    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
            Commerce, incorporated by reference to Exhibit 10.1 of Cole National
            Corporation's Quarterly Report on Form 10-Q for the period ended May
            2, 1998 (File 1-12814)

                                      -10-