Molecular dynamic simulations of nanoindentation were performed to investigate the effects of graphene coatings on the plastic deformation of copper (Cu) under different indentation conditions. The results show that the graphene coating can dramatically strengthen the load bearing capability of Cu substrate for the displacement-controlled indentation, which is proportional to the number of graphene layers increasing from single to triple. And the load force also increases with the rising indentation speed, causing larger and rapider plastic deformation. For the load-controlled indentation, the graphene coating can protect the Cu substrate from being damaged by the external force. The protection capability of graphene increases as the layers growing to triple at the same loading. What's more, the larger load force can facilitate the increase in penetration depth at the equilibrium state. Our observation provide a better understanding of mechanism of plastic deformation under the effect of graphene covering.