In this paper, we specify a powerful way to boost quantum capacitance of graphene-based electrode materials by density functional theory calculations. We performed functionalization of graphene to manifest high-quantum capacitance. A marked quantum capacitance of above 420 $\mu$F cm$^{−2}$ has been observed. Our calculations show that quantum capacitanceof graphene enhances with nitrogen concentration. We have also scrutinized effect on the increase of graphene quantum capacitance due to the variation of doping concentration, configuration change as well as co-doping with nitrogen and oxygen ad-atoms in pristine graphene sheets. A significant increase in quantum capacitance was theoretically detected in functionalized graphene, mainly because of the generation of new electronic states near the Dirac point and the shift of Fermi level caused by ad-atom adsorption.