Graphene nanoribbon on copper (G/Cu) based interconnect has shown superior electro-thermal transport as a potential candidate for the next generation interconnects. Using density function theory (DFT) we have studied the capacitance of graphene/copper (G/Cu) hybrid-nano wire interconnect system and compared with graphene-based interconnect. From the first principle calculation, band structure and density of states have been calculated. Quantum capacitance is calculated from the density of states of G/Cu hybrid material. For this presented G/Cu system, we found significant enhancement in quantum capacitance which indicates a dominance of electrostatic capacitance over quantum capacitance in overall interconnect capacitances. Near Dirac point, a 5nm wide G/Cu nanoribbon shows a capacitance of 25.29 µF/cm 2 while its 2D counterpart shows only 4.75 µF/cm 2 . For comparison, a 2D graphene sheet shows only 0.06 µF/cm 2 .