A three-dimensional kinetic Monte Carlo technique has been developed for simulating growth of thin Cu films. The model involves incident atom attachment, diffusion of the atoms on the growing surface, and detachment of the atoms from the growing surface. The related effect by surface atom diffusion was taken into account. A great improvement was made on calculation of the activation energy for atom diffusion based on a reasonable assumtion of interaction potential between atoms. The surface roughness and the relative density of the films were simulated as the functions of growth substrate temperature and film thickness. The results showed that there exists an optimum growth temperatureT opt at a given deposition rate. When the substrate temperature approaches toT opt, the growing surface becomes smoothing and the relative density of the films increases. The surface roughness minimizes and the relative density saturates atT opt. The surface roughness increases with an increment of substrate, temperature when the temperature is higher thanT opt.T opt is a function of the deposition rate and the influence of the deposition rate on the surface roughness depends on the substrate temperatures. The simulation results also showed that the relative density decreases with the increasing of the deposition rate and the average thickness of the film.