Exhibit 32.1

SECTION 1350 CERTIFICATION OF THE CHIEF EXECUTIVE OFFICER,

CHIEF FINANCIAL OFFICER, AND CHIEF ACCOUNTING OFFICER/CONTROLLER

In connection with the Quarterly Report on Form 10-Q of Nash-Finch Company, (the “Company”) for the 12 weeks ended March 23, 2013 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, Alec C. Covington, President and Chief Executive Officer, Robert B. Dimond, Executive Vice President, Chief Financial Officer and Treasurer, and Peter J. O’Donnell, Chief Accounting Officer/Controller, respectively, of the Company, certify, pursuant to 18. U.S.C. Section 1350, that to our knowledge:

(1)the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of the dates and for the periods expressed in the Report. 

Date:   April 25, 2013                                                        

By:  /s/Alec C. Covington                                                                 

Name: Alec C. Covington

Title: President and Chief Executive Officer

By:  /s/ Robert B. Dimond                                                                

Name:  Robert B. Dimond

Title:  Executive Vice President, Chief Financial Officer and Treasurer

By:  /s/ Peter J. O’Donnell                                                                 

Name:  Peter J. O’Donnell

Title:  Chief Accounting Officer/Controller