CONSTRUCTION PARTNERS, INC.

     LIMITED POWER OF ATTORNEY FOR SECTION 13 AND SECTION 16 FILINGS

        I, Ned N. Fleming, III, of 5420 LBJ Freeway, Suite 1000, Dallas, Texas
75240, do hereby make, constitute and appoint Charles E. Owens and R. Alan
Palmer, my true and lawful attorneys for the purposes hereinafter set forth,
effective as of this 3rd day of May, 2018.

        References in this limited power of attorney to "my Attorney" are to
each of the persons named above and to the person or persons substituted
hereunder pursuant to the power of substitution granted herein.

        I hereby grant to my Attorney, for me and in my name, place and stead,
the power:

     1. To execute for and on my behalf, in my capacity as a stockholder of
        Construction Partners, Inc., a Delaware corporation (the "Company"), any
        Schedule 13D and Schedule 13G, and all and any amendments thereto, in
        accordance with Section 13 of the Securities Exchange Act of 1934 and
        the rules and regulations promulgated thereunder (the "Exchange Act");

     2. To execute for and on my behalf, in my capacity as an officer, director
        and/or stockholder of the Company, Form 3, Form 4, and Form 5, and all
        and any amendments thereto, in accordance with Section 16(a) of the
        Exchange Act;

     3. To do and to perform any and all acts for and on my behalf that may be
        necessary or desirable to complete and execute any such Schedule 13D,
        Schedule 13G, Form 3, Form 4 and Form 5, or any amendment thereto, and
        to timely file such schedule, form or amendment thereto with the United
        States Securities and Exchange Commission (the "SEC") and any stock
        exchange or similar authority; and

     4. To take any other action of any type whatsoever that, in the opinion of
        my Attorney, may be necessary or desirable in connection with the
        foregoing grant of authority, it being understood that the documents
        executed by my Attorney pursuant to this limited power of attorney shall
        be in such form and shall contain such terms and conditions as my
        Attorney may approve.

        I hereby grant to my Attorney full power and authority to do and to
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 I might or could do if personally present,
with full power of substitution or revocation, hereby ratifying and confirming
all that my Attorney shall lawfully do or cause to be done by virtue of this
limited power of attorney and the rights and powers herein granted. I
acknowledge and agree that neither my Attorney nor the Company is assuming any
of my responsibilities to comply with the Exchange Act.

        This limited power of attorney shall remain in full force and effect
until I am no longer required to file any Schedule 13D, Schedule 13G, Form 3,
Form 4 or Form 5 with respect to my holdings of, and transactions in, securities
of the Company, unless earlier revoked by me in a signed writing delivered to
each of my Attorneys and the substitutes therefore, if any. This limited power
of attorney may be filed with the SEC as a confirming statement of the authority
granted herein.

        IN WITNESS WHEREOF, I have hereunto set my hand to this instrument on
the date first above written.

                                        /s/ Ned N. Fleming, III
                                        ------------------------------
                                        Ned N. Fleming, III

STATE OF New York
COUNTY OF New York

        Before me, Rhonda Gerolmo-Miller, on this day personally appeared Ned
N. Fleming, III, known to me to be the person whose name is subscribed to the
foregoing instrument and acknowledged to me that he executed the same for the
purposes and consideration therein expressed.

Given under my hand and seal of office this 30th day of April, 2018.

Rhonda Gerolmo-Miller
------------------------------
Notary Public

My Commission Expires: November 4, 2018

[Affix Notary Seal]