EXHIBIT 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO SECTION 906

OF THE SARBANES-OXLEY ACT OF 2002

I, Kevin M. Freeman, state and attest that:

(1) I am the President and Chief Executive Officer of Old Dominion Freight Line, Inc. (the “Issuer”).

(2) Accompanying this certification is the Issuer’s Quarterly Report on Form 10-Q for the quarter ended March 31, 2024 (the “Quarterly Report”), a periodic report filed by the Issuer with the Securities and Exchange Commission pursuant to Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), which contains financial statements.

(3) I hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge:

◦ The Quarterly Report containing the financial statements fully complies with the requirements of Section 13(a) or 15(d) of the Exchange Act, and

◦ The information contained in the Quarterly Report fairly presents, in all material respects, the financial condition and results of operations of the Issuer for the periods presented.