Power of Attorney

        Know all by these presents, that the undersigned hereby constitutes and
appoints each of Edward Miller, Vikas Sinha and Brett Hagen, signing singly, and
with full power of substitution, as the undersigned's true and lawful attorney-
in-fact to:

           (1) execute for and on behalf of the undersigned, in the
           undersigned's capacity as an officer and/or director of AlloVir,
           Inc., a Delaware corporation (the "Company"), from time to time the
           following Securities and Exchange Commission (the "SEC") forms: Forms
           3, 4, and 5 in accordance with Section 16(a) of the Securities
           Exchange Act of 1934, as amended (the "Exchange Act"), and the rules
           thereunder;

           (2) 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

           (3) 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 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 each 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 power of attorney and the
rights and powers herein granted. The undersigned acknowledges that the
foregoing attorneys-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 Exchange Act.

        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 attorneys-in- fact. This Power of Attorney shall expire as to any
individual attorney-in-fact if such attorney-in-fact ceases to be an officer of
the Company. This Power of Attorney may be filed with the SEC as a confirming
statement of the authority granted herein.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 29th day of July 2020.


              /s/ Malcolm Brenner
              ---------------------------
Printed Name: Malcolm Brenner