UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934

(Amendment No. 2)*

R.G. Barry Corporation

(Name of Issuer)

Common Stock, par value $1 per share

(Title of Class of Securities)

068798107

(CUSIP Number)

Mill Road Capital II, L.P.

Attn: Thomas E. Lynch

382 Greenwich Avenue

Suite One

Greenwich, CT 06830

203-987-3500

With a copy to:

Peter M. Rosenblum, Esq.

Foley Hoag LLP

155 Seaport Blvd.

Boston, MA 02210

617-832-1151

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)

September 11, 2013

(Date of Event Which Requires Filing of This Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box.  ¨

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See §240.13d-7 for other parties to whom copies are sent.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

13D

13D

13D

13D

This Amendment No. 2 to the joint statement on Schedule 13D with respect to the common stock, par value $1 per share (the “Common Stock”), of R.G. Barry Corporation, an Ohio corporation (the “Issuer”), filed by Mill Road Capital, L.P., a Delaware limited partnership (“Fund I”), Mill Road Capital GP LLC, a Delaware limited liability company (“GP I”), Thomas E. Lynch and Scott P. Scharfman (collectively, the “Initial Reporting Persons”) on February 18, 2011 (the “Schedule 13D”), as amended and restated by the Amendment No. 1 on Schedule 13D with respect to the Common Stock filed by the Initial Reporting Persons, Mill Road Capital II, L.P. and Mill Road Capital II GP LLC on August 29, 2012 (such joint statement, as so amended and restated and as amended herein, the “Schedule 13D”), further amends the Schedule 13D as follows.

‘This joint statement on Schedule 13D is being filed by Thomas E. Lynch, Scott P. Scharfman, Mill Road Capital II, L.P., a Delaware limited partnership (“Fund II”), and Mill Road Capital II GP LLC, a Delaware limited liability company (“GP II”). Each of Fund II, GP II, and Messrs. Lynch and Scharfman is referred to in this Schedule 13D as a “Reporting Person” and, collectively, as the “Reporting Persons.” GP II is the sole general partner of Fund II. Messrs. Lynch and Scharfman, Charles M. B. Goldman and Justin C. Jacobs are the management committee directors of GP II and, in these capacities, are referred to in this Schedule 13D as the “Managers.”’

‘The Reporting Persons have acquired beneficial ownership of an aggregate of 968,189 shares of Common Stock for $15,009,349.02 using working capital from Fund II and the proceeds of margin loans under margin loan facilities maintained in the ordinary course of business by Fund II with a broker on customary terms and conditions. As described in Item 5 below, each of GP II and Messrs. Lynch and Scharfman has beneficial ownership of these shares of Common Stock by having sole or shared dispositive and investment power over them.’

‘On September 11, 2013, the Management Company sent the letter attached hereto as Exhibit 4 to the Issuer’s Board of Directors. In the letter, the Management Company and its affiliated funds offered to acquire all shares of the Common Stock at a cash price of $20.00 per share.’

‘(a, b) The percentages of beneficial ownership reported in this Item 5, and on the respective cover pages to the Schedule 13D of each Reporting Person, are based on a total of 11,290,894 shares of the Common Stock issued and outstanding as of May 8, 2013, as reported in the most recent quarterly report of the Issuer on Form 10-Q for the fiscal quarter ended March 30, 2013. All of the share numbers reported below, and on these cover pages, are as of September 11, 2013, unless otherwise indicated. Each of these cover pages is incorporated by reference in its entirety into this Item 5(a, b).

Fund II directly holds, and thus has sole voting and dispositive power over, 968,189 shares of Common Stock. GP II, as sole general partner of Fund II, also has sole authority to vote (or direct the vote of), and to dispose (or direct the disposal) of, these shares of Common Stock on behalf of Fund II, and each of Messrs. Lynch and Scharfman has shared authority to vote (or direct the vote of), and to dispose (or direct the disposal) of, the shares of Common Stock on behalf of Fund II. Messrs. Goldman and Jacobs do not have beneficial ownership of any shares of Common Stock.

Accordingly, each of the Reporting Persons beneficially owns 968,189 shares of Common Stock, or approximately 8.6% of the outstanding shares of Common Stock, and the Reporting Persons beneficially own, in the aggregate, 968,189 shares of Common Stock, or approximately 8.6% of the outstanding shares of Common Stock.

(c) No Reporting Person, other than Fund II as set forth in the table below, effected any transaction in shares of the Common Stock from July 13, 2013 (the date 60 days prior to the filing of this amendment to the Schedule 13D) to September 11, 2013.

Each transaction was conducted in the ordinary course of business on the open market for cash. Purchases have been aggregated daily, and purchase prices do not reflect brokerage commissions paid.

(d) No person other than the Reporting Persons is known to have the right to receive or the power to direct the receipt of dividends from or the proceeds from the sale of shares of the Common Stock.

(e) Not applicable.’

‘Exhibit 4 Letter from Mill Road Capital Management LLC to the Board of Directors of R.G. Barry Corporation Re: Notice of Acquisition Proposal dated September 11, 2013.’

Signature

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

Exhibit 4

September 11, 2013   Board of Directors R.G. Barry Corporation 13405 Yarmouth Road N.W. Pickerington, Ohio 43147   Re:     Notice of Acquisition Proposal

Members of the Board:

Mill Road Capital Management LLC and its affiliated funds (“Mill Road”) are long time shareholders of R.G. Barry Corporation (the “Company,”), as evidenced by our initial average public market acquisition price of $6.73 per share for our more than six hundred and forty thousand shares.

As one of the Company’s largest shareholders for many years we have always been highly impressed with the Company and its management team. We think Greg Tunney has done an outstanding job as CEO and leads a strong and deep bench of talented people. However, despite the Company’s many strengths, we think that the public market will never accord a high valuation to R.G. Barry. It is a small company with limited opportunities to gain market share in a very low growth core market. In addition, the Company’s strategy to pursue growth through acquisitions in other markets has delivered very slow results to public investors. We further believe that by remaining public the Company will continue to incur regulatory costs and burdens disproportionate to its size. R.G. Barry will therefore be better able to realize its full potential as a private entity.

Accordingly, Mill Road is pleased to submit an offer to acquire all shares of the Company’s stock at a cash price of $20.00 per share. This price represents a premium of 24% to the last 30 days average closing price of $16.17, and we believe is a noteworthy premium to any price at which the stock has traded in the last 45 years.

Mill Road is an investment firm focused exclusively on investments in small value-based publicly-traded companies, and over the last several years Mill Road has completed more going private capital transactions with these companies than any other firm. We know the Company well and are prepared to commence negotiation of definitive agreements and business, financial and legal due diligence immediately. We expect that with the cooperation of the Company, the period required to complete our due diligence will be brief. Needless to say, this offer is not binding on Mill Road; binding legal obligations of Mill Road and the Company will be created only through execution and delivery of definitive agreements.

You may contact me directly at (203) 987-3504. I look forward to discussing our proposal at your earliest convenience.

Sincerely,

Mill Road Capital Management LLC