Here, to increase the conductivity and the electrochemical performance of copper oxide electrodes, D-sorbitol assisted ball-mill synthesized graphene is utilized and copper oxide/graphene supercapacitor electrode materials are prepared in an environmentally benign solvothermal-assisted method. The characterization studies indicated the formation of well-dispersed Cu2O and CuO over less-defective few layered graphene with strong Cu-O-C interactions and the electrochemical studies indicated the synergistic effect of copper oxides and graphene in the supercapacitor performance of the electrodes. The nanocomposite in its best composition of copper oxides with graphene showed the highest specific capacitance of 1589 F/g at a current density of 2 A/g and 100 % capacitance retention after 10,000 continuous charge discharge cycles. The diffusive contribution to the capacitance of the nanocomposite is greater due to the pseudocapacitive effect of copper oxides. The symmetrical coin cell fabricated using copper oxide/graphene showed a specific capacitance of 27.23 mF/cm2 at a current density of 0.01 mA/cm2. The practical applicability of the fabricated supercapacitor devices in lighting up a red LED is also displayed here.