In this paper, the homotopy perturbation method (HPM) proposed by J. H. He is adopted for solving multi-dimensional non-linear coupled system of parabolic and hyperbolic equations. The numerical results of the present method are compared with the exact solution of an artificial multi-dimensional non-linear coupled system of parabolic and hyperbolic model to show the efficiency of the method. Moreover, comparison are made between the results obtained by the present method and that obtained by Adomian decomposition method (ADM). It is found that the present method works extremely well, very efficient, simple and convenient.