A three-dimensional kinetic Monte-Carlo technique has been developed for simulating the growth of thin Cu films. The model involves incident atom attachments, diffusion of the atoms on the growing surface, and the detachment of the atoms from the growing surface. Related effects due to 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 assumption of interaction potential between atoms. The results showed that as the substrate temperature is raised or the deposited rate decreased, the diffusion of particles causes the particles grouping into islands (more than three atoms). The higher the temperature or the lower the deposition rate, the larger the size of the islands. Also we observed the island shape transition from two-dimensional islands to three-dimensional ones. There exist three optimum growth temperatures at a given deposition rate, namely Tn at which the nucleation rate is maximum, Tr at which the surface roughness minimizes and Td at which the relative density approaches to saturation. They all increase with the increase of substrate temperature, and these variations almost superpose on each other. The simulation results also showed that the relative density decreases with increasing deposition rate. But the nucleation rate is close to a steadiness at a lower temperature while it increases at a higher temperature. The surface roughness increases at a lower temperature while it decreases at a higher temperature.