Dynamic effects, such as steering and screening during deposition, on epitaxial growth (Cu/Cu (001)) were studied by kinetic Monte Carlo simulations that incorporate molecular dynamics simulations to account for the interaction between the deposited and substrate atoms. Three characteristics of the surface morphology with grazing angle deposition were noted: enhanced surface roughness, an asymmetric mound, and asymmetric slopes of the mound sides. Regarding their dependence on both deposition angle and substrate temperature, reasonable agreement was found between the simulation and previous experimental results. The growth characteristics of grazing angle deposition were mainly caused by inhomogeneous distribution of deposition flux due to the steering and screening effects, with the steering effects playing the dominant role. It was also noted in the present simulation that each side of a mound was composed of various local facets instead of a selected facet. Thus, slope selection does not necessarily signify facet selection.