Summary: In this paper we deal with a one-dimensional free boundary problem, which is a mathematical model for an adsorption phenomena appearing in concrete carbonation process. This model was proposed in line of previous studies of three dimensional concrete carbonation process. The main result in this paper is concerned with the existence and uniqueness of a time-local solution to the free boundary problem. This result will be obtained by means of the abstract theory of nonlinear evolution equations and Banach’s fixed point theorem, and especially, the maximum principle applied to our problem will play a very important role to obtain the uniform estimate to approximate solutions.