Molecular dynamics simulations of nanoindentation are performed to investigate the strengthening mechanisms of graphene coatings on Cu film substrate. It is found that the load bearing capacity of Cu substrate can be evidently improved after covering graphene coatings, and this turns out to be proportional to the number of graphene layers from monolayer to trilayer. The strengthening mechanism of elastic stage mainly results from the stress homogenization effect generated by graphene interface. Moreover, the efficiency of graphene strengthening during plastic stage is much higher than the elastic stage. The interactions between dislocations and graphene coating interface are fully responsible for the strengthening increase of Cu/graphene system in the plastic stage. In addition, a theoretical model to predict the strength of Cu/graphene system depending on the confined layer slip (CLS) model is established.