We investigated the structural and electrical properties of B-, N-, and Si-doped graphene/Cu interfaces through density functional theory. B-doping enhances the interfacial bonding strength, N-doping has little effect on the interfacial interaction, and Si-Cu bonds are formed in the Si-doped interface. The energy bands and density of states show that the pristine and N-doped graphene/Cu interfaces exhibit n-type semiconductor properties, and the B-doped and Si-doped graphene/Cu interfaces exhibit p-type semiconductor properties. According to the Mulliken charge populations and charge properties, B-doping and Si-doping improve the ability of charge transport and orbital hybridization at the interface. Graphene doping has a significant effect on the interfacial work function. This result will help to understand the contact between B-, N-, and Si-doped graphene and Cu surfaces and to predict the performance of related micro-nano electronic devices.