POWER OF ATTORNEY

        Know all by these present, that the undersigned hereby constitutes and
appoints each of Ankit Mahadevia, Chief Executive Officer of Spero Therapeutics,
Inc. (the "Company"), Joel Sendek, Chief Financial Officer of the Company, and
Stephen Garbacz, Senior Vice President of Finance and Operations of the Company,
and Matthew J. Gardella, Matthew W. Tikonoff, Leah J. Pollema, Brian J. Shea,
Anne T. Leland and Brenda L. Meyette of Mintz, Levin, Cohn, Ferris, Glovsky and
Popeo, P.C., signing singly, with full power of substitution, the undersigned's
true and lawful attorney-in-fact to:

        (1) execute for and on behalf of the undersigned, forms and
            authentication documents for EDGAR Filing Access;

        (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 forms and authentication documents;

        (3) execute for and on behalf of the undersigned, in the
            undersigned's capacity as an officer, director and/or 10%
            shareholder of the Company, Forms 3, 4 and 5 in accordance with
            Section 16(a) of the Securities Exchange Act of 1934 and the rules
            thereunder;

        (4) 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 and timely file such form with the United States
            Securities and Exchange Commission and any stock exchange or similar
            authority; and

        (5) 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 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 attorneys-in- fact.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed this 2nd day of August, 2018.


                                        /s/  John C. Pottage, Jr.
                                        ---------------------------------
                                        John C. Pottage, Jr.