Under investigation in this paper is a reaction-diffusion system, which describes acid-mediated tumor growth. First, in view of Lie group analysis, infinitesimal generators of the considered system are presented. At the same time, some group invariant solutions are computed using reduced equations. In particular, we construct explicit solutions by applying the power-series method. Furthermore, the convergence of the solutions of the power-series is certificated. Finally, the stability behavior of the model can be understood by analyzing the solutions of different parameters.