Supercapacitor is an energy storage device which obtains energy from the electrochemical double layer or the redox-type reactions at or beyond the surface of the electrode, which can meet the demands for high power and long cycle life. However, the electrode still has low energy density for supercapacitor device. The design of electrode material is essential for obtaining high capacity. We employ density functional theory based on the first principle to calculate the electronic structures and derive the capacitance of N-doping graphene. We find that the quantum capacitance can be substantially improved by N doping. The physical mechanism of such phenomena is discussed in this paper.