We have investigated the growth mode of thin films on substrates with a faceted surface structure of a nanometer scale by means of computer simulations. The simulations have been performed for various combinations of the growth parameters such as the substrate temperature, the lattice mismatch between the film and the substrate, the interaction between the him and substrate atoms. In order to perform realistic growth simulations we have developed the molecular dynamics (MD) aided kinetic Monte Carlo (KMC) method. In the method MD deals with non-equilibrium structural relaxation of surface clusters and KMC deals with thermally activated adatom migrations. The film growth is classified into three types. The growth is promoted in the valley region or in the ridge region, or it has no site preference, depending on the growth parameters. The relation between the film growth on faceted substrates and that on flat substrates is discussed.