Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statement on Form S-8 (File No. 333-162695) of our report dated June 27, 2013, with respect to the financial statements and supplemental schedule of the Old Dominion 401(k) Retirement Plan included in this Annual Report on Form 11-K as of December 31, 2012 and 2011 and for the year ended December 31, 2012.

/s/ Dixon Hughes Goodman LLP

High Point, North Carolina

June 27, 2013