The growth of clusters on an inhomogeneous substrate is simulated by using Monte Carlo method. The inhomogeneous substrate is composed of two different kinds of regularly distributed materials A and B with different physical properties. Deposited particles have initial energy E0. It consumes energies EA and EB when a particle diffuses one step on phases A and B, respectively, and it consumes energy EAB when the particle passes through the phase boundary from A to B. In the simulation, E0 is much bigger than EA and EB, and the energy needed for the particle to pass through the phase boundary from B to A is set as EBA=0. Results show that the clusters aggregated on the inhomogeneous substrate are of fractal structure. When EAB is much bigger than EA and EB, the number, radius of gyration and fractal dimension of the cluster all vary periodically with ratio E0/EBA.