We applied molecular dynamics, density functional theory, and computer graphics techniques to the investigation of the homoepitaxial growth process of the MgO(001) surface. MgO molecules are deposited over the MgO(001) plane one by one at regular time intervals with definite velocities. Any deposited MgO molecule migrated on the surface, and later a two-dimensional and epitaxial growth of MgO thin layer was observed at 300 K which is in agreement with the experimental result. However, some defects were constructed in the grown film at low temperature of 300 K, which is in remarkable contrast to that at 1000 K. In the latter case, a single flat and smooth MgO layer without defects was formed, which also agreed with the experimental result. Self-diffusion coefficients and activation energy for the surface diffusion of the deposited MgO molecule on the MgO(001) plane were discussed to clarify the temperature-dependency of the epitaxial growth process.