The growth mechanism of Co atoms on Cu atomic substrates was studied by molecular dynamics simulation with large scale atomic/polar massively parallel simulator (LAMMPS). The embedded atom method (EAM) potential was used to investigate the growth processes of Co atoms on different Cu atom configurations. The growth process of Co on Cu substrate was carefully observed. It was found that Co atoms preferentially grow on the (100) facet on the Wulff configuration. To find out under what conditions the core-shell structure is better formed, the number of Cu atoms adsorbed on the surface and the number of Co atoms entering the interior were calculated as a function of the number of deposited atoms. The Wulff configuration was found to be more favorable for the growth of Co atoms on the Cu substrates. And the effect of the size of the Cu substrate on the growth of the Co atoms was also investigated. The results show that the larger the size of the Cu substrate, the more unfavorable the core-shell structure formation. In addition, the effect of temperature on growth was also analyzed. It was found that the higher the temperature, the more unfavorable the growth.