The present work includes the fabrication and electrochemical characterization of cobalt oxide (Co3O4)/graphene nanosheets nanocomposite as efficient electrode for supercapacitor application. The characterization techniques involved in this work are scanning electron microscopy and transmission electron microscopy for surface morphology, Raman spectroscopy and X-Ray diffraction for structural analysis. The specific capacitance of Co3O4 with multilayer graphene nanocomposite was determined to be 140 F/g (28 mF/cm2) at scan rate of 20 mV/s. The composite electrode can deliver a power density of 856 W/kg with maintaining energy density of 2.38 Wh/kg. The better performance is due to the synergistic effect of graphene and Co3O4 in the composite.