A kinetic Monte Carlo model describing the three-dimensional thin film growth on heterogeneous substrates is presented, in which the diffusion of adatoms on substrates, along the island edges and between various layers, as well as the heterogeneity of adsorptive energy, are taken into account. Three growth modes, namely the Layer-by-layer mode, Stranski-Krastanovs mode and 3D mode, and the morphology of multiple layer growth of thin films are simulated. The relationship between thin film growth modes and growth conditions is established by taking into account the distribution of deposited atoms on various layers and the surface roughness of thin films.