The existence of defects on the substrate surface is unavoidable and has a significant impact on the determination of surface properties. Among the prevalent types of defects, steps play an important role. In this study, molecular dynamics simulations are employed to explore the growth process of a thin film of Cu on a Si (001) substrate with a step. This research investigates how incident energy and thermal annealing affect the growth mode, surface roughness, film-substrate interface, and dislocation evolution. The results indicate that during the initial stage of the growth, the nucleation phenomenon was observed on terraces. The simulation indicates that the Cu atoms occur in an island growth mode on the stepped substrate. It is found that when the incident energy is increased and thermal annealing is performed, the surface curvature and roughness are reduced. Furthermore, the intermixing thickness at the interface increases due to the variation of the incidence energy. A dislocation analysis revealed that some dislocations disappeared before and after annealing, and a perfect dislocation appeared by increasing the incident energy.