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 20, 2018, with respect to the financial statements and supplemental schedules of the Old Dominion 401(k) Retirement Plan included in this Annual Report on Form 11-K for the fiscal year ended December 31, 2017.

/s/ Dixon Hughes Goodman LLP

High Point, North Carolina

June 20, 2018