Graphene characterized with ultrahigh intrinsic strength and excellent electronic properties is an ideal material to reinforce metals without despairing their thermal and electrical properties. Here, the electronic and mechanical properties of graphene intercalated copper (graphene/Cu) composites are investigated using density functional theory calculations. Graphene/Cu systems present an excellent electrical conductivity and increasing Debye temperature from 335 K for pure Cu to over 535 K in regardless of stacking models. In addition to greatly enhanced Young's modulus (149%), shear modulus (156%) and bulk modulus (108%) compared to copper, the ultimate strength of graphene/Cu composites are enhanced by 174% and 162%, in x and y directions, respectively. The strengthening and toughening effects of graphene in the composites is originated from strain strengthening and load transfer, which is consistent with the experimental results. Based on this calculation, the strengthening mechanism can be understood, which explains many experimental observations and also provides us a guide to improve graphene/metal composites quality.