<PAGE>   1
                       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 April 25, 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 1-13380
                                                -------

                                OFFICEMAX, INC.
                                ---------------
             (Exact name of registrant as specified in its charter)

                  OHIO                                  34-1573735
                  ----                                  ----------
   (State or other jurisdiction of                   (I.R.S. Employer 
    incorporation or organization)                   Identification No.)

           3605 WARRENSVILLE CENTER ROAD, SHAKER HEIGHTS, OHIO 44122
           ---------------------------------------------------------
                    (Address of principal executive offices)
                                   (zip code)

                                 (216) 921-6900
                                 --------------
              (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. Yes X   No    .
                                                           ----   ----

         Indicate the number of shares outstanding of each of the
         issuer's classes of common stock, as of the latest practical
         date.
 
       Title of Class                             Shares Outstanding as of
       --------------                                  May 15, 1998
        Common Shares                                  ------------
     (without par value)                               124,712,154


<PAGE>   2

                           OFFICEMAX, INC.

                                INDEX


<TABLE>
<CAPTION>
Part I - Financial Information                                        Page
------------------------------                                        
 
<S>    <C>                                                           <C> 
       Item 1. Financial Statements                                   3-7

       Item 2. Management's Discussion and Analysis of Financial     8-10
               Condition and Results of Operations



<CAPTION>
Part II - Other Information
---------------------------

<S>    <C>                                                           <C> 
        Item 6. Exhibits and Reports on Form 8-K                      11


      Signatures                                                      12
</TABLE>


                                        2
<PAGE>   3


                    PART I - FINANCIAL INFORMATION
                    
ITEM 1. FINANCIAL STATEMENTS
----------------------------

                           OFFICEMAX, INC.
                     CONSOLIDATED BALANCE SHEETS
                        (Dollars in thousands)
                             (Unaudited)


<TABLE>
<CAPTION>
                                                               April 25,          Jan.24,
                                                                 1998             1998
ASSETS                                                       ------------     ------------
<S>                                                          <C>              <C>         
Current Assets:
 Cash and equivalents                                        $     44,933     $     66,801
 Accounts receivable, net of allowances
  of $796 and $837, respectively                                   44,615           38,221
 Merchandise inventories                                        1,113,698        1,086,228
 Other current assets                                              50,400           37,255
                                                             ------------     ------------
   Total current assets                                         1,253,646        1,228,505

Property and Equipment:
 Buildings and land                                                19,155           19,212
 Leasehold improvements                                           174,803          172,878
 Furniture and fixtures                                           302,804          287,728
                                                             ------------     ------------
 Total property and equipment                                     496,762          479,818
 Less: Accumulated depreciation and amortization                 (183,045)        (167,965)
                                                             ------------     ------------
 Property and equipment, net                                      313,717          311,853
Other assets and deferred charges                                  41,991           41,280
Goodwill, net of accumulated amortization
 of $53,579 and $51,231, respectively                             322,007          324,355
                                                             ------------     ------------
                                                             $  1,931,361     $  1,905,993
                                                             ============     ============

LIABILITIES AND SHAREHOLDERS' EQUITY
Current Liabilities:
 Accounts payable - trade                                    $    439,663     $    442,390
 Accrued expenses and other liabilities                           142,748          128,674
 Accrued salaries and related expenses                             34,452           38,669
 Taxes other than income taxes                                     54,283           55,953
 Mortgage loan, current portion                                     1,300            1,300
                                                             ------------     ------------
   Total current liabilities                                      672,446          666,986
Mortgage loan                                                      17,400           17,725
Other long-term liabilities                                        59,670           60,637
                                                             ------------     ------------
   Total liabilities                                              749,516          745,348

Commitments and contingencies

Shareholders' Equity:
  Common shares, without par value; 200,000,000 shares
    authorized; 124,594,551 and 124,370,209 shares issued         864,186          861,991
    and outstanding, respectively
  Deferred stock compensation                                        (375)            (306)
  Retained earnings                                               319,313          300,239
  Less: Treasury stock                                             (1,279)          (1,279)
                                                             ------------     ------------
      Total shareholders' equity                                1,181,845        1,160,645
                                                             ------------     ------------
                                                             $  1,931,361     $  1,905,993
                                                             ============     ============
</TABLE>

The accompanying Notes to Consolidated Financial Statements are an integral part
                            of these balance sheets.



                                        3
<PAGE>   4

                                 OFFICEMAX, INC.
                     CONSOLIDATED STATEMENTS OF OPERATIONS
                 (Dollars in thousands, except per share data)
                                  (Unaudited)





<TABLE>
<CAPTION>
                                                             13 Weeks Ended
                                                  --------------------------------
                                                  April 25, 1998    April 26, 1997
                                                  --------------    --------------
<S>                                               <C>               <C>           
Sales                                             $    1,061,074    $      888,640
Cost of merchandise sold, including
 buying and occupancy costs                              818,736           688,869
                                                  --------------    --------------

Gross profit                                             242,338           199,771

Store operating and selling expenses                     183,026           151,483
Pre-opening expenses                                       1,759             2,237
General and administrative expenses                       24,240            19,301
Goodwill amortization                                      2,346             2,347
                                                  --------------    --------------

   Total operating expenses                              211,371           175,368

Operating income                                          30,967            24,403

Interest income, net                                         197             1,299

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

Income before income taxes                                31,164            25,702

Income taxes                                              12,090             9,972
                                                  --------------    --------------

Net income                                        $       19,074    $       15,730
                                                  ==============    ==============

EARNINGS PER COMMON SHARE DATA:

Basic Earnings per common share                   $         0.15    $         0.13
                                                  ==============    ==============

Weighted average number of
   common shares outstanding                         124,472,062       123,093,270
                                                  ==============    ==============

Diluted Earnings per common share                 $         0.15    $         0.13
                                                  ==============    ==============

Weighted average number of
   common shares outstanding                         127,049,856       124,788,296
                                                  ==============    ==============
</TABLE>







       The accompanying Notes to Consolidated Financial Statements are an
                       integral part of these statements.

                                       4
<PAGE>   5


                                OFFICEMAX, INC.
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                             (Dollars in thousands)
                                  (Unaudited)



<TABLE>
<CAPTION>
                                                                    13 Weeks Ended
                                                              --------------------------
                                                               April 25,      April 26, 
                                                                 1998           1997
                                                              ----------      ----------
<S>                                                           <C>             <C>       
CASH PROVIDED BY (USED FOR):

OPERATIONS
     Net income                                               $   19,074      $   15,730
     Adjustments to reconcile net income to net cash from
      operating activities:
      Depreciation and amortization                               17,445          15,390
      Increase (decrease) in deferred income taxes                   514            (501)
      Increase (decrease) in other long-term liabilities            (966)            925
      Other, net                                                    (504)            287
     Change in current assets and current liabilities:
      (Increase) decrease in inventories                         (27,470)          2,839
      Decrease in accounts payable                                (2,728)        (59,366)
      Increase in accounts receivable                             (6,394)        (19,908)
      Decrease in accrued liabilities                            (59,714)        (45,849)
                                                              ----------      ----------
           Net cash (used for) operations                        (60,743)        (90,453)
                                                              ----------      ----------

INVESTING
     Capital expenditures                                        (28,201)        (33,953)
     Other, net                                                   (1,294)         (1,636)
                                                              ----------      ----------
           Net cash (used for) investing                         (29,495)        (35,589)
                                                              ----------      ----------

FINANCING
     Payments of mortgage principal                                 (325)             --
     Increase in revolving credit facility                        66,500              --
     Proceeds from issuance of common stock, net                   2,195           1,134
                                                              ----------      ----------
           Net cash provided by financing                         68,370           1,134
                                                              ----------      ----------

CASH AND CASH EQUIVALENTS
     Net (decrease) for the period                               (21,868)       (124,908)
     Balance, beginning of period                                 66,801         258,111
                                                              ----------      ----------
     Balance, end of period                                   $   44,933      $  133,203
                                                              ==========      ==========

SUPPLEMENTAL INFORMATION
     Interest paid on debt                                    $      422      $       --
                                                              ==========      ==========
     Taxes paid on income                                     $   14,782      $   16,487
                                                              ==========      ==========
</TABLE>

The accompanying Notes to Consolidated Financial Statements are an integral part
                              of these statements.





                                       5
<PAGE>   6

                                OFFICEMAX, INC.
           CONSOLIDATED STATEMENT OF CHANGES IN SHAREHOLDERS' EQUITY
                             (Dollars in thousands)
                                  (Unaudited)

<TABLE>
<CAPTION>
                                         Common Shares           Deferred
                                 ----------------------------      Stock         Retained       Treasury
                                    Shares          Amount      Compensation     Earnings         Stock          Total
                                 -------------  -------------  --------------  -------------  --------------  -------------
<S>                               <C>            <C>            <C>             <C>            <C>             <C>        
Balance at January 24, 1998       124,370,209    $   861,991    $      (306)    $   300,239    $    (1,279)    $ 1,160,645

Issuance of common shares
  under director plan                     364              7             (7)              -              -               -

Exercise of stock options             164,203          1,324              -               -              -           1,324
(including tax benefit)

Sale/(forfeiture) of shares
under management share                 45,572            652           (130)              -              -             522
purchase plan (including tax
benefit)

Sale of shares under employee          14,203            212              -               -              -             212
share purchase plan (including
tax benefit)

Amortization of deferred                    -              -             68               -              -              68
  compensation

Net income                                  -              -              -          19,074              -          19,074
                                 -------------  -------------  --------------  -------------  --------------  -------------
Balance at April 25, 1998         124,594,551    $   864,186    $      (375)    $   319,313    $    (1,279)    $ 1,181,845
                                 =============  =============  ==============  =============  ==============  =============
</TABLE>




The accompanying Notes to Consolidated Financial Statements are an integral part
                              of these statements.



                                       6
<PAGE>   7

                                 OFFICEMAX, INC.
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                             FOR THE 13 WEEKS ENDED
                       APRIL 25, 1998 AND APRIL 26, 1997



Significant Accounting and Reporting Policies
---------------------------------------------


1.   The accompanying consolidated financial statements have been prepared from
     the financial records of OfficeMax, Inc. and its subsidiaries (the
     "Company" or "OfficeMax") without audit and reflect all adjustments which
     are, in the opinion of management, necessary to fairly present the results
     of the interim periods covered in this report. The results for any interim
     period are not necessarily indicative of the results to be expected for the
     full fiscal year.

2.   The Company's consolidated financial statements for the 13 weeks ended
     April 25, 1998 and April 26, 1997 included in this Quarterly Report on Form
     10-Q, have been prepared in accordance with the accounting policies
     described in the Notes to Consolidated Financial Statements for the fiscal
     year ended January 24, 1998 which were included in the Company's Annual
     Report on Form 10-K filed with the Securities and Exchange Commission (File
     No.1-13380) on April 21, 1998. Certain information and footnote disclosures
     normally included in financial statements prepared in accordance with
     generally accepted accounting principles have been condensed or omitted in
     accordance with the rules and regulations of the Securities and Exchange
     Commission. These financial statements should be read in conjunction with
     the financial statements and the notes thereto included in the Form 10-K
     referred to above. Certain reclassifications have been made to prior year
     amounts to conform to the current presentation.

3.   The Company's fiscal year ends on the Saturday prior to the last Wednesday
     in January.

4.   At April 25, 1998, OfficeMax operated a chain of 733 superstores in over
     300 markets, 48 states and Puerto Rico, as well as two national call
     centers, 17 delivery centers and OfficeMax retail joint ventures in Mexico
     and Japan.

5.   The Company's policy is to expense pre-opening expenses during the first
     month of each new store's operation. Consequently, pre-opening expense in
     each period is generally a function of the number of new stores opened
     during that period.

6.   The average common and common equivalent shares utilized in computing
     diluted earnings per share for the 13 weeks ended April 25, 1998 and April
     26, 1997 include 2,479,392 and 907,093 shares, respectively, resulting from
     the application of the treasury stock method to outstanding stock options.


                                       7
<PAGE>   8

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


RESULTS OF OPERATIONS
---------------------

SALES for the 13 weeks ended April 25, 1998 increased 19% to $1,061,074,000 from
$888,640,000 for the comparable period a year earlier. The sales increase was
attributable to a full period of sales from the 150 stores opened during fiscal
1997, the additional sales from 20 new superstores opened at various points
during the 13-week period and a comparable store sales increase of 2% during the
13-week period. Excluding computers, same-store sales for the 13 weeks increased
7% over last year's first quarter. Comparable store sales were negatively
impacted by deflationary prices in computers, printers and fax machines along 
with the Company's deliberate decision to drastically curtail computer 
promotions.

GROSS PROFIT for the 13 weeks ended April 25, 1998, was 22.8% as compared to
22.5% for the same period a year earlier. The increase in gross profit resulted
from the Company's continued focus on increasing margin productivity of its core
office supplies and furniture business while at the same time improving the
profitability of its computer and electronic sales by modifying the product and
promotional offerings.

STORE OPERATING AND SELLING EXPENSES, which consist primarily of store payroll,
operating and advertising expenses, increased as a percentage of sales to 17.3%
for the 13 weeks ended April 25, 1998, from 17.1% of sales for the same period a
year earlier. The Company experienced a decrease in leverage of these items
primarily due to a greater number of immature stores as the percentage of stores
opened less than one year. New stores typically begin to leverage the fixed cost
components in their second year of operations. This increase in costs was
partially offset by improved leveraging of advertising expenses as the Company
opened additional stores in existing markets.

PRE-OPENING EXPENSE was $1,759,000 for the 13 weeks ended April 25, 1998, as
compared to $2,237,000 for the same period a year earlier, reflecting the
opening of 20 superstores during the 13 weeks ended April 25, 1998, compared to
23 superstores for the same period last year. Pre-opening expenses in the first
quarter averaged approximately $85,000 per store, as compared to an average of
approximately $75,000 per store for the prior year. Pre-opening expenses
consist primarily of store payroll, supplies and grand opening advertising. For
the 13 weeks ended April 25, 1998, the Company also opened 2 FurnitureMax hubs
and 1 CopyMax hub, for which pre-opening expenses averaged approximately $25,000
and $35,000, respectively, per store.

GENERAL AND ADMINISTRATIVE EXPENSES were 2.3% of sales for the 13 weeks ended
April 25, 1998, as compared to 2.2% of sales for the same period a year ago.
This increase reflects the Company's continuing efforts to strengthen and
enhance its infrastructure and management team to support the planned growth
both in the United States and internationally.

GOODWILL AMORTIZATION was $2,346,000 for the 13 weeks ended April 25, 1998, as
compared to $2,347,000 for the same period a year earlier. Goodwill is
capitalized and amortized over 40 years using the straight-line method.

OPERATING INCOME increased to $30,967,000 or 2.9% of sales, for the 13 weeks
ended April 25, 1998, as compared to operating income of $24,403,000 or 2.8% of
sales, for the same period a year earlier.

INTEREST INCOME, NET was $197,000 for the 13 weeks ended April 25, 1998, as
compared to $1,299,000 for the same period a year earlier. Interest income
decreased due to the Company's continued use of cash and cash equivalents to
fund its aggressive expansion plans. The Company expects to incur net interest
expense for fiscal 1998, as the line of credit is used periodically during the
year to fund seasonal merchandise needs.



                                       8
<PAGE>   9

INCOME TAXES were $12,090,000 for the 13 weeks ended April 25, 1998, as
compared to $9,972,000 for the same period a year ago. The effective tax rates
for both periods are different from the federal statutory income tax rate
primarily as a result of goodwill amortization, tax exempt interest, and state
and local taxes.

NET INCOME as a result of the foregoing factors, was $19,074,000 for the 13
weeks ended April 25, 1998, as compared to $15,730,000 for the same period a
year earlier.

LIQUIDITY AND CAPITAL RESOURCES
-------------------------------

Net cash used for operations for the 13 weeks ended April 25, 1998 was
$60,743,000. Major uses of working capital included increases in inventory and
a decrease in accrued liabilities. The inventory increase was attributable to
new store openings and the build-up of merchandise for the Company's new
275,000-square-foot merchandise distribution facility in Las Vegas, Nevada. Net
cash used for investing activities was $29,495,000, principally due to capital
expenditures for new and remodeled stores as well as the Company's continued
investment in systems. Net cash received from financing was $68,370,000,
primarily representing borrowings under the Company's $500,000,000 revolving
credit facility.

During the 13 weeks ending July 25, 1998, the Company plans to open
approximately 20 new OfficeMax superstores and remodel 4 existing superstores.
The Company also plans to open 2 new CopyMax and 2 new FurnitureMax hubs.
These are store-within-a-store modules devoted exclusively to print-for-pay
services and office furniture, respectively. Management estimates that the
Company's cash requirements for these openings and remodels, exclusive of
pre-opening expenses, will be approximately $1,200,000, $140,000, $350,000, and
$250,000, respectively, for each additional OfficeMax, FurnitureMax, CopyMax,
and store remodel. For an OfficeMax superstore, the requirements include an
average of approximately $450,000 for leasehold improvements, fixtures,
point-of-sales terminals and other equipment, and approximately $750,000 for the
portion of store inventory that is not financed by accounts payable to vendors.
Pre-opening expenses are expected to average approximately $85,000 for an
OfficeMax superstore, $25,000 for a FurnitureMax module and $35,000 for a
CopyMax module.

In order to finance its operations and capital requirements, including its
expansion strategy, the Company expects to use funds generated from operations
as well as its current cash reserves, and, to the extent necessary, seasonal
short-term borrowings. The Company has available through June 2002 a
$500,000,000 revolving credit facility. As of April 25, 1998, the Company had
outstanding borrowings of $66,500,000 under the revolving credit facility.

The Company did not acquire any of its shares through open market purchases
during the 13 weeks ended April 25, 1998. Depending on the Company's cash
position and market conditions, the Company may acquire common shares in the
future under the stock repurchase program that was approved by the Board of
Directors in November 1997.

The Company has undertaken a comprehensive review of its computer-based systems
and applications to identify modifications necessitated by the century change
for the year 2000 and has implemented a plan to make such modifications. The
Company intends to have all critical systems compliant with the century change
prior to the end of 1999 at a cost of approximately $1,000,000.

The Company's business is somewhat seasonal, with sales and operating income
higher in the third and fourth quarters, which include the Back-to-School period
and the holiday selling season, respectively, followed by the traditional new
year office supply restocking month of January. Sales in the second quarter's
summer months are the slowest of the year primarily because of lower office
supplies consumption during the summer vacation period.



                                       9
<PAGE>   10

CAUTIONARY STATEMENT REGARDING FORWARD-LOOKING INFORMATION
----------------------------------------------------------

Certain statements contained in "Management's Discussion and Analysis of
Financial Condition and Results of Operations" and elsewhere in this report
constitute "forward-looking statements" within the meaning of Section 27A of the
Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934.
These forward-looking statements are based upon management's expectations and
beliefs concerning future events and discuss, among other things, expected
growth and future business plans. Words and phrases such as "expects",
"anticipates", "believes", "intends", "estimates", "will likely result", "will
continue", "plans to" and similar expressions are intended to identify
forward-looking statements. Readers are cautioned not to place undue reliance on
any forward-looking statements. Forward-looking statements are necessarily
subject to risks, uncertainties and other factors, many of which are outside the
control of the Company, that could cause actual results to differ materially
from such statements. A discussion of these risks, uncertainties and other
factors is included in the Company's Annual Report on Form 10-K filed with the
Securities and Exchange Commission. Any forward-looking statement speaks only as
of the date on which such statement is made, and the Company undertakes no
obligation to update any forward-looking statement, whether as a result of new
information, future events or otherwise.






































                                       10
<PAGE>   11

                           PART II- OTHER INFORMATION



ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
----------------------------------------

Exhibits:

(a)  Exhibits:

              27.0    Financial Data Schedule for the period ended April 25, 
                      1998

(b)  Reports on Form 8-K:  None







































                                       11
<PAGE>   12

                                   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.

<TABLE>
<S>                                  <C>
                                      OFFICEMAX, INC.

Date: June 4, 1998                     By: /s/ Jeffrey L. Rutherford
                                          --------------------------------------
                                           Jeffrey L. Rutherford
                                           Executive Vice President, Chief Financial Officer
                                           (Principal Financial Officer and
                                            Principal Accounting Officer)
</TABLE>

















                                       12