Two-dimensional MoS2 is a promising candidate for high performance electrochemical capacitors. However, the understanding of different capacitive performances of MoS2 with different phases is still limited. Herein, the pseudocapacitive and electrical double layer characters in T and H phases of MoS2 monolayer are systematically studied, by using first-principles calculations and molecular dynamic simulations. The electronic levels referenced to the vacuum level are utilized to discuss the intrinsic pseudocapacitive characters. The large density of states of T-MoS2 located at 0.25V versus the standard hydrogen electrode indicates possible redox pseudocapacitance. Contrastively, the large band gap of H-MoS2 limits its pseudocapacitive behavior. Furthermore, the reaction with the Li atom is employed to shed more light on the possible redox behavior. The different shifts of Fermi levels in H and T phase confirm their different capacitive properties. Moreover, the electrical double layer capacitances character of MoS2 in aqueous solution is also investigated. The H-MoS2 exhibits similar double layer character with T-MoS2. The calculated double layer capacitances of MoS2 are comparable with graphene, and can reach 9.07μF/cm2 and 7.42μF/cm2 for anode and cathode, respectively. The combined calculations shed more light to explore other two-dimensional transition-metal dichalcogenides as supercapacitors electrode materials.