In this paper we define and study a finite volume scheme for a concrete carbonation model proposed by Aiki and Muntean in [Adv. Math. Sci. Appl. 19 (2009) 109–129]. The model consists in a system of two weakly coupled parabolic equations in a varying domain whose length is governed by an ordinary differential equation. The numerical sheme is obtained by a Euler discretisation in time and a Scharfetter-Gummel discretisation in space. We establish the convergence of the scheme. As a by-product, we obtain existence of a solution to the model. Finally, some numerical experiments show the efficiency of the scheme.