Asymmetric supercapacitors with high energy density are fabricated using a self-assembled reduced graphene oxide (RGO)/MnO2 (GrMnO2) composite as a positive electrode and a RGO/MoO3 (GrMoO3) composite as a negative electrode in safe aqueous Na2SO4 electrolyte. The operation voltage is maximized by choosing two metal oxides with the largest work function difference. Because of the synergistic effects of highly conductive graphene and highly pseudocapacitive metal oxides, the hybrid nanostructure electrodes exhibit better charge transport and cycling stability. The operation voltage is expanded to 2.0 V in spite of the use of aqueous electrolyte, revealing a high energy density of 42.6 Wh kg−1 at a power density of 276 W kg−1 and a maximum specific capacitance of 307 F g−1, consequently giving rise to an excellent Ragone plot. In addition, the GrMnO2//GrMoO3 supercapacitor exhibits improved capacitance with cycling up to 1000 cycles, which is explained by the development of micropore structures during the repetition of ion transfer. This strategy for the choice of metal oxides provides a promising route for next-generation supercapacitors with high energy and high power densities.