Molecular dynamics simulations of nanolaminated graphene/Cu (NGCu) and pure Cu under compression are conducted to investigate the underlying strengthening mechanism of graphene and the effect of lamella thickness. It is found that the stress-strain curves of NGCu undergo 3 regimes i.e. the elastic regime I, plastic strengthening regime II and plastic flow regime III. Incorporating graphene monolayer is proved to simultaneously contribute to the strength and ductility of the composites and the lamella thickness has a great effect on the mechanical properties of NGCu composites. Different strengthening mechanisms play main role in different regimes, the transition of mechanisms is found to be related to the deformation behavior. Graphene affected zone is developed and integrated with rule of mixtures and confined layer slip model to describe the elastic properties of NGCu and the strengthening effect of the incorporated graphene.