LIMITED POWER OF ATTORNEY

        Know all by these presents that the undersigned, Anita D. Britt, hereby
constitutes and appoints the duly appointed Secretary of VSE Corporation,
Farinaz S. Tehrani, as the undersigned's true and lawful attorney-in-fact to:

        (1)   prepare, execute in the undersigned's name and on the
              undersigned's behalf, and submit to the United States Securities
              and Exchange Commission (the "SEC") one or more Forms ID,
              including any amendments thereto, and any other documents
              necessary or appropriate to obtain, update or maintain codes,
              passwords or passphrases enabling the undersigned to make
              electronic filings with the SEC of reports required by Section
              16(a) of the Securities Exchange Act of 1934 or any rule or
              regulation of the SEC;

        (2)   execute for and on behalf of the undersigned, in the
              undersigned's capacity as a director and/or officer of VSE
              CORPORATION (the "Company"), Forms 3, 4, and 5 in accordance with
              Section 16(a) of the Securities Exchange Act of 1934 and the
              rules thereunder;

        (3)   do and perform any and all acts for and on behalf of the
              undersigned which may be necessary or desirable to complete and
              execute any such Form 3, 4, or 5, complete and execute any
              amendment or amendments thereto, and timely file such form with
              the SEC and any stock exchange or similar authority; and

        (4)   take any other action of any type whatsoever in connection with
              the foregoing which, in the opinion of such attorney-in-fact, may
              be of benefit to, in the best interest of, or legally required
              by, the undersigned, it being understood that the documents
              executed by such attorney-in-fact on behalf of the undersigned
              pursuant to this Limited Power of Attorney shall be in such form
              and shall contain such terms and conditions as such attorney-in-
              fact may approve in such attorney-in-fact's discretion.

        The undersigned hereby grants to such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might
or could do if personally present, with full power of substitution or
revocation, hereby ratifying and confirming all that such attorney-in-fact, or
such attorney-in-fact's substitute or substitutes, shall lawfully do or cause
to be done by virtue of this Limited Power of Attorney and the rights and
powers herein granted. The undersigned acknowledges that the foregoing
attorney-in-fact, in serving in such capacity at the request of the
undersigned, is not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 16 of the Securities
Exchange Act of 1934.

        This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorney-in-fact.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney
to be executed as of this 18th day of July, 2022.

                                   /s/ Anita D. Britt
                                   --------------------------------------
                                   Anita D. Britt