Cu/graphene nanosheets composites were fabricated at 800°C by the hot-pressing method using Cu and graphene as initial materials. Graphene content was 1 wt. %-5 wt. %. The fracture morphology and physical properties of the composites were investigated. It was found that the relative density increased with the increment of graphene content from 1 wt% to 5 wt. % with reaching its highest level (96.68%) at 5wt. %. The composites have the anisotropic property which is vertical to the direction of pressure is higher than parallel to the direction of pressure. With the increasing of graphene content, the thermal conductivity property and the electronic conductivity decrease first and then increase with the minimum thermal conductivity and electric conductivity at 3wt%~4wt%.