A new molecular dynamics (MD) code was developed to simulate the continuous deposition process of various molecules on substrates. In this methodology, various molecules can be deposited over substrate surfaces one by one in regular time intervals with definite velocity. It enables us to simulate homo- and hetero-epitaxial growth process as well as cluster formation process on various substrates. This new MD code has been already applied to study the homoepitaxial growth and Au cluster formation processes on MgO(00l). This article compares such phenomena as growth mode, temperature effect, and influence of surface defects in the homoepitaxial growth and Au cluster formation processes on the MgO(001), based on previous results. The continuous deposition process of MgO molecules was simulated. A 2–D smooth MgO layer without any defects was formed at 1,000 K, which was not realized at 300 K. High temperature is favorable for the complete layer-by-layer homoepitaxial growth. The deposition process of Au atoms on the Mg(001) differed significantly from that of MgO molecules. A 3-D hemispherical Au cluster was constructed on the MgO(001) and low temperature was found to be desired for the fabrication of highly active supported Au catalysts. The origin of the different growth mode and the different temperature effect in the homo-epitaxial growth and Au cluster formation on the MgO(001) was clarified.