The graphene islands, formed as different sizes, are crucial for the final quality of the formed graphene during the CVD growth either as the nucleation seeds or as the build blocks for larger graphene domains. Extensive efforts had been devoted to the size or the morphology control while fewer works were reported on the moving dynamics of these graphene islands as well as the associate influences to their coalescence during the CVD Growth of graphene. In this study, based on the self-developed C-Cu empirical potential, we performed systematic molecular dynamics simulations on the surface moving of three typical graphene islands CN (N = 24, 54 and 96) on the Cu (111) surface and discovered their different behaviors in sinking, lateral translation and rotation at the atomic scale owning to their different sizes, which were proved to bring forth significant impacts to their coalescences and the final quality of the as-formed larger domains of graphene. This study would deepen our atomistic insights into the mechanisms of the graphene CVD growth and provide significant theoretical guidelines to its controlled synthesis.