<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        July 4, 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 1-8769
                                                 ------

                             R. G. BARRY CORPORATION
                             -----------------------
             (Exact name of registrant as specified in its charter)

              OHIO                                              31-4362899
--------------------------------------------------------------------------------
  (State or other jurisdiction                                (IRS Employer
of incorporation or organization)                         Identification Number)

  13405 Yarmouth Road, NW, Pickerington, Ohio                      43147
--------------------------------------------------------------------------------
    (Address of principal executive office)                      (Zip Code)

                                  614-864-6400
                                  ------------
              (Registrant's telephone number, including area code)

                                 NOT APPLICABLE
                                 --------------
              (Former name, former address, and former fiscal year,
                          if changed since last report)

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

     Common Shares, $1 Par Value, Outstanding as of July 4, 1998 - 9,691,706
                                                    ------------------------

                          Index to Exhibits at page 10

                               Page 1 of 14 pages
<PAGE>   2
<TABLE>
                                PART I - FINANCIAL INFORMATION
                                 ITEM 1 - FINANCIAL STATEMENTS
                           R. G. BARRY CORPORATION AND SUBSIDIARIES
                                  CONSOLIDATED BALANCE SHEETS
<CAPTION>
                                                               July 4, 1998   January 3, 1998
                                                               ------------   ---------------
                                                                       (in thousands)
<S>                                                              <C>               <C>
ASSETS:
   Cash and cash equivalents                                     $  2,387          22,495
   Accounts receivable, less allowances                            10,713          16,961
   Inventory (note 3)                                              59,613          35,602
   Deferred income taxes (note 4)                                   4,827           4,827
   Recoverable income taxes                                         1,113              --
   Prepaid expenses                                                 2,668           2,669
                                                                 --------         -------
         Total current assets                                      81,321          82,554
                                                                 --------         -------

   Property, plant and equipment, at cost                          41,599          40,840
      Less accumulated depreciation & amortization                 27,600          26,609
                                                                 --------         -------
         Net property, plant and equipment                         13,999          14,231
                                                                 --------         -------

   Goodwill, less accumulated amortization                          4,172           4,230
   Other assets                                                     3,852           3,659
                                                                 --------         -------
                                                                 $103,344         104,674
                                                                 ========         =======

LIABILITIES AND SHAREHOLDERS' EQUITY:
   Current installments of long-term debt
      and capital lease obligations                                 2,273           2,273
   Short-term notes payable                                        10,500            --
   Accounts payable                                                 8,042           6,389
   Accrued expenses                                                 1,607          11,355
                                                                 --------         -------
      Total current liabilities                                    22,422          20,017
                                                                 --------         -------

   Accrued retirement costs and other, net                          4,472           4,057

   Long-term debt and capital lease obligations,
      excluding current installments:
      Note payable                                                 10,714          12,857
      Capital lease obligations                                       135             135
                                                                 --------         -------
         Long-term debt and capital lease obligations              10,849          12,992
                                                                 --------         -------
            Total liabilities                                      37,743          37,066
                                                                 --------         -------

   Shareholders' equity:
      Preferred shares, $1 par value
         Authorized 3,775,000 Class A shares,
         225,000 Series I Junior Participating Class A
         shares, and 1,000,000 Class B shares, none issued
      Common shares, $1 par value
         Authorized 22,500,000 shares
         (excluding treasury shares)                                9,692           9,564
      Additional capital in excess of par value                    15,061          14,629
      Deferred compensation (note 6)                                 (218)           --
      Retained earnings                                            41,066          43,415
                                                                 --------         -------
         Net shareholders' equity                                  65,601          67,608
                                                                 --------         -------
                                                                 $103,344         104,674
                                                                 ========         =======
</TABLE>

                               Page 2 of 14 pages
<PAGE>   3
<TABLE>
                             R. G. BARRY CORPORATION AND SUBSIDIARIES
                              CONSOLIDATED STATEMENTS OF OPERATIONS
<CAPTION>
                                           Thirteen weeks ended          Twenty-six weeks ended
                                           --------------------          ----------------------
                                          July 4,        June 28,        July 4,        June 28,
                                           1998            1997           1998           1997
                                           ----            ----           ----           ----
                                                              (in thousands)
<S>                                       <C>             <C>            <C>            <C>   
Net sales                                 $16,910         14,511         32,503         29,474
Cost of sales                               8,180          7,623         13,626         14,227
                                          -------         ------         ------         ------
   Gross profit                             8,730          6,888         18,877         15,247
Selling, general and
   administrative expense                  11,103          9,577         22,440         19,664
                                          -------         ------         ------         ------
Operating loss                             (2,373)        (2,689)        (3,563)        (4,417)

Other income                                   87             98            191            243

Interest expense                             (401)          (450)          (784)          (827)
Interest income                                24             32            241            203
                                          -------         ------         ------         ------
   Net interest expense                      (377)          (418)          (543)          (624)

Loss before
   tax benefit                             (2,663)        (3,009)        (3,915)        (4,798)
Income tax benefit (note 4)                (1,065)        (1,203)        (1,566)        (1,919)
                                          -------         ------         ------         ------
   Net loss                               $(1,598)        (1,806)        (2,349)        (2,879)
                                          =======         ======         ======         ======

Net loss per common share (note 5)
      Basic                               $ (0.16)         (0.19)         (0.24)         (0.30)
                                          =======         ======         ======         ======
      Diluted                             $ (0.16)         (0.19)         (0.24)         (0.30)
                                          =======         ======         ======         ======

Average number of common
   shares outstanding
      Basic                                 9,695          9,489          9,647          9,451
                                          =======         ======         ======         ======
      Diluted                               9,695          9,489          9,647          9,451
                                          =======         ======         ======         ======
</TABLE>

                               Page 3 of 14 pages
<PAGE>   4
<TABLE>
                           R. G. BARRY CORPORATION AND SUBSIDIARIES
                        CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOW
<CAPTION>
                                                                Twenty-six        Twenty-six
                                                               weeks ended       weeks ended
                                                              July 4, 1998     June 28, 1997
                                                              ------------     -------------
                                                                       (in thousands)
<S>                                                             <C>               <C>    
Cash flows from operating activities:
   Net loss                                                     $ (2,349)         (2,879)
   Adjustments to reconcile net loss to net cash
      used in operating activities:
      Depreciation and amortization of
         property, plant and equipment                               871             831
      Amortization of goodwill                                        58              58
      Net (increase) decrease in:
         Accounts receivable, net                                  6,248           9,951
         Inventory                                               (24,011)        (21,843)
         Prepaid expenses                                              1            (493)
         Recoverable income taxes                                 (1,113)         (1,558)
         Other                                                      (193)             35
      Net increase (decrease) in:
         Accounts payable                                          1,653           3,170
         Accrued expenses                                         (9,748)         (7,032)
         Accrued retirement costs and other                          415             406
                                                                --------         -------
            Net cash used in operating activities                (28,168)        (19,354)
                                                                --------         -------

Cash flows from investing activities:
   Additions to property, plant and equipment, net                  (639)         (1,031)
                                                                --------         -------

Cash flows from financing activities:
   Proceeds from short-term notes                                 10,500           9,000
   Stock options exercised, net of treasury acquisitions             342             500
   Repayment of long-term debt and
      capital lease obligations                                   (2,143)              0
                                                                --------         -------
         Net cash provided by financing activities                 8,699           9,500
                                                                --------         -------

Net decrease in cash                                             (20,108)        (10,885)
Cash at the beginning of the period                               22,495          13,187
                                                                --------         -------
Cash at the end of the period                                   $  2,387           2,302
                                                                ========         =======

Supplemental cash flow disclosures:
   Interest paid                                                $  1,532             789
                                                                ========         =======
   Income taxes paid                                            $  6,933           3,904
                                                                ========         =======
</TABLE>

                               Page 4 of 14 pages
<PAGE>   5
                    R. G. BARRY CORPORATION AND SUBSIDIARIES
                          Notes to Financial Statements
                       Under Item 1 of Part I of Form 10-Q
                              for the Periods ended
                         July 4, 1998 and June 28, 1997

1.   These interim financial statements are unaudited. All adjustments
     (consisting solely of normal recurring adjustments) have been made which,
     in the opinion of management, are necessary to fairly present the results
     of operations.

2.   The Company operates on a fifty-two or fifty-three week annual fiscal year.
     Fiscal 1998 is a fifty-two week year, fiscal 1997 was a fifty-three week
     year.

3.   A substantial portion of inventory is valued using the dollar value LIFO
     method and, therefore, it is impractical to separate inventory values
     between raw materials, work-in-process and finished goods.

4.   Income tax benefit for the periods ended July 4, 1998 and June 28, 1997,
     consists of:

                                                   1998              1997
                                                   ----              ----
                     Current:
                          U. S. Federal          $(1,335)          $(1,612)
                          State & Local             (231)             (307)
                                                 -------           -------
                               Total             $(1,566)          $(1,919)
                                                 =======           =======

     The income tax benefit reflects a combined federal, foreign, state and
     local effective rate of 40.0 percent for both years, as compared to the
     statutory U. S. federal rate of 35.0 percent in both years.

     Income tax for the periods ended July 4, 1998 and June 28, 1997 differed
     from the amounts computed by applying the U. S. federal income tax rate of
     35.0 percent to pretax loss as a result of the following:

                                                            1998         1997
                                                            ----         ----
                     Computed "expected"
                       tax benefit:
                          U. S. Federal benefit           $(1,370)      $(1,631)
                          Other                               (46)          (85)
                          State & Local benefit, net of
                            federal income tax benefit       (150)         (203)
                                                          -------       -------
                               Total                      $(1,566)      $(1,919)
                                                          =======       =======


5.   The computation of basic loss per common share has been computed based on
     the weighted average number of common shares outstanding during each
     period. Diluted loss per common share is based on the weighted average
     number of outstanding common shares during the period, plus, when their
     effect is dilutive, potential common shares consisting of certain common
     shares subject to stock options and the stock purchase plan.

6.   Pursuant to agreements with two key executives, entered into in January
     1998, the Company is committed to issue a total of 10,000 common shares to
     each executive ratably over the next eight years, subject to the terms of
     the agreement. Upon achievement of certain profit goals in any fiscal year,
     the issuance of common shares may be accelerated. The Company will expense
     the costs associated with the agreements over the eight-year term of the
     agreements.

                               Page 5 of 14 pages
<PAGE>   6
                    R. G. BARRY CORPORATION AND SUBSIDIARIES
      ITEM 2 - Management's Discussion and Analysis of Financial Condition
                            and Results of Operations

Liquidity and Capital Resources
-------------------------------
The Company ended the second quarter of 1998 with $58.9 million in net working
capital. This compares with $51.6 million at the end of the same quarter in
1997, and $62.5 million at the end of fiscal 1997. The increase in net working
capital from the end of the second quarter of 1997 to the end of the second
quarter of 1998, is mostly due to the profit that the Company earned during
fiscal 1997. The decline in working capital from fiscal year end 1997 to the end
of the second quarter of 1998, is mainly the result of the seasonal loss
incurred during the second quarter of 1998, plus the scheduled periodic payment
on long-term debt made during the quarter.

Highlights of the significant changes in the components of the Company's net
working capital are:


o    Accounts receivable increased at the end of the second quarter of 1998, to
     $10.7 million from $8.6 million at the end of the second quarter of 1997,
     and decreased from $17.0 million at the end of fiscal 1997. The increase in
     receivables from second quarter 1997 to the second quarter of 1998, is
     mainly due to the increase in net sales of 16.5 percent during the second
     quarter of 1998 when compared with the same quarter of 1997. The decrease
     from the end of fiscal 1997, represents a normal seasonal pattern of change
     in receivables.

o    Inventories at the end of the second quarter of 1998, at $59.6 million, are
     about 17.6 percent greater than the inventory levels of $50.7 million one
     year ago, and increased from $35.6 million as of the end of fiscal 1997.
     The increase in inventories from the end of the second quarter of 1997 to
     the end of the second quarter of 1998 represents increases in varying
     elements of the Company's inventories [raw materials, work in-process and
     finished goods] as the Company builds its operations in Europe and plans
     for its future domestic growth needs. The increase in inventories from the
     end of fiscal 1997, reflects normal seasonal patterns of inventories in
     anticipation of supporting sales later in the year.

o    The Company ended the second quarter of 1998, with $2.4 million in cash and
     $10.5 million in short-term bank loans. This compares with the second
     quarter of 1997, when the Company had $2.3 million in cash and $9 million
     in short-term bank loans. The increase in short-term bank loans is largely
     a result of borrowing under the Company's short-term Revolving Credit
     Agreement to meet a scheduled long-term debt payment, due for the first
     time in the life of the loan at the end of June, 1998. There were no
     short-term bank loans outstanding at the end of fiscal 1997.

The Company's capital expenditures during the first half of 1998, amounted to
$639 thousand, compared with $1.0 million during the same period of 1997.
Capital expenditures in both years have been funded out of working capital.

The Company currently has in place a Revolving Credit Agreement ("Revolver"),
with its three main lending banks. The Revolver provides the Company a
seasonally adjusted available line of credit ranging from $6 million during
January, to a peak of $51 million from July through November. The Revolver
contains financial covenants typical of agreements of its type and duration. The
Company is in compliance with all the covenants of the Revolver, and all other
debt agreements. The Revolver, previously extended through 1999, contains
provisions for periodic extensions upon request and with the approval of the
banks. Subsequent to the end of the second quarter, the Revolver was extended
through 2000.

Results of Operations
---------------------
During the second quarter of 1998, net sales amounted to $16.9 million, an
increase of 16.5 percent from the $14.5 million during the second quarter of
1997. For the six months, net sales amounted to $32.5 million, a 10.3 percent
increase in net sales when compared with the first six months of 1997. Net sales
of the Company's slipper products, domestically and internationally, were
largely responsible for the increases in consolidated net sales.

                               Page 6 of 14 pages
<PAGE>   7
           Management's Discussion and Analysis of Financial Condition
                      and Results of Operations - continued


Gross profit during the second quarter of 1998, amounted to $8.7 million, or
51.6 percent of net sales. This compares with gross profit percent of 47.5
percent in the same quarter of 1997. For the six months, gross profit percent
also increased to 58.1 percent in 1998 compared with 51.7 percent in 1997. The
increase in gross profit percentages from year to year, is mainly due to the
Company's continuing efforts in the area of cost reduction such as the expanded
use of modular manufacturing, and a change in mix of individual styles and
products sold from year to year.

Selling, general and administrative expenses during the quarter amounted to
$11.1 million, an increase of 15.9 percent from the same quarter one year ago.
For the six months these expenses amounted to $22.4 million, an increase of 14.1
percent from the same six months last year. The percentage increases are in line
with the percentage increases in net sales for the periods. Included in these
expenses are the costs of the Company's expansion in the French slipper markets,
which began in the fourth quarter of 1997.

Net interest expense declined from 1997 to 1998. During the second quarter of
1998, net interest expense amounted to $377 thousand compared with $418 thousand
in the same period of 1997. For the six months, net interest expense also
declined to $543 thousand in 1998 from $624 thousand in 1997. The decrease in
net interest expense is principally due to the Company's lower average usage of
its Revolver during 1998, when compared with 1997.

For the second quarter of 1998, the Company incurred a net loss of $1.6 million,
or $0.16 per share, compared with a net loss during the same quarter of 1997 of
$1.8 million, or $0.19 per share. For the six months, the Company incurred a net
loss in 1998 of $2.3 million, or $0.24 per share, compared with a net loss in
1997 of $2.9 million, or $0.30 per share. Per share calculations for both years
are the same for both basic loss per share and for diluted loss per share.


--------------------------------------------------------------------------------
"SAFE HARBOR" STATEMENT UNDER THE PRIVATE SECURITIES LITIGATION REFORM ACT OF
1995:
The statements in this Quarterly Report on Form 10-Q, which are not historical
fact are forward looking statements based upon the Company's current plans and
strategies, and reflect the Company's current assessment of the risks and
uncertainties related to its business, including such things as product demand
and market acceptance; the economic and business environment and the impact of
governmental regulations, both in the United States and abroad; the effects of
competitive products and pricing pressures; currency risks; capacity,
efficiency, and supply constraints; weather conditions; and other risks detailed
in the Company's press releases, shareholder communications, and Securities and
Exchange Commission filings. Actual events affecting the Company and the impact
of such events may vary from those currently anticipated.
--------------------------------------------------------------------------------


     ITEM 3 - Quantitative and Qualitative Disclosures About Market Risk
Not Applicable

                               Page 7 of 14 pages
<PAGE>   8
                           PART II - OTHER INFORMATION

Item 1.  Legal Proceedings
--------------------------
         No response required

Item 2.  Changes in Securities and Use of Proceeds
--------------------------------------------------
         (a) through (d) Not Applicable

Item 3.  Defaults Upon Senior Securities
----------------------------------------
         (a), (b) Not Applicable

Item 4.  Submission of Matters to a Vote of Security Holders
------------------------------------------------------------
         (a) The Annual Meeting of Shareholders of the Company (the "Annual
         Meeting") was held on May 13, 1998. At the close of business on the
         record date, March 16, 1998, 9,593,488 common shares were outstanding
         and entitled to vote at the Annual Meeting. At the Annual Meeting,
         8,711,801 or 90.8% of the outstanding common shares entitled to vote
         were represented in person or by proxy.

         (b) Directors elected at the Annual Meeting were:

             Edward M. Stan
             For:             8,672,570
             Withheld:           39,231             Broker non-vote:   none

             Richard L. Burrell
             For:             8,669,882
             Withheld:           41,919             Broker non-vote:   none

             Philip G. Barach
             For:             8,675,499
             Withheld:           36,302             Broker non-vote:   none

             Other directors whose term of office continued after the Annual
             Meeting:
             Gordon Zacks                           Harvey M. Krueger
             Christian Galvis                       William Giovanello
             Charles E. Ostrander                   Leopold Abraham II

         (c) See Item 4(b) for the voting results for directors

         (d) Not Applicable

Item 5.  Other Information
--------------------------
         As discussed in the Company's Proxy Statement for the Annual Meeting,
         any qualified shareholder of the Company who intends to submit a
         proposal to the Company at the 1999 Annual Meeting of Shareholders must
         submit such proposal to the Company no later than November 27, 1998 to
         be considered for inclusion in the Company's Proxy Statement and form
         of Proxy ("Proxy") relating to that meeting. If a shareholder intends
         to present a proposal at the 1999 Annual Meeting of Shareholders, but
         has not sought the inclusion of such proposal in the Company's Proxy,
         such proposal must be received by the Company prior to February 27,
         1999 or the Company's management proxies for the 1999 Annual Meeting
         will be entitled to use their discretionary voting authority should
         such proposal then be raised, without any discussion of the matter in
         the Company's Proxy.

Item 6.  Exhibits and Reports on Form 8-K
-----------------------------------------
         (a) Exhibits: See Index to Exhibits at page 10.

         (b) Reports on Form 8-K: No reports on Form 8-K were filed during the
         quarter ended July 4, 1998.

                               Page 8 of 14 pages
<PAGE>   9
                                   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.


                                              R. G. BARRY CORPORATION
                                              -----------------------
                                              Registrant

August 04, 1998                               /s/ Richard L. Burrell
---------------                               ----------------------
     date                                     Richard L. Burrell
                                              Senior Vice President - Finance
                                              (Principal Financial Officer)
                                              (Duly Authorized Officer)

                               Page 9 of 14 pages
<PAGE>   10
<TABLE>
                                     R. G. BARRY CORPORATION
                                        INDEX TO EXHIBITS
<CAPTION>
  Exhibit No.                         Description                                   Page Number
  -----------                         -----------                                   -----------
<S>              <C>                                                                  <C>
       4         Agreement to Extend Revolving Credit Agreement,                      11 - 12
                 dated as of May 20, 1998, among the Registrant, The
                 Bank of New York, The Huntington National Bank, and
                 NBD Bank

     27.1        Financial Data Schedule                                                13
                 (Period ended July 4, 1998)

     27.2        Financial Data Schedule                                                14
                 (Period ended June 28, 1997 Restated)
</TABLE>

                               Page 10 of 14 pages