The graphene–manganese oxide hybrid material has been prepared by solution-phase assembly of aqueous dispersions of graphene nanosheets and manganese oxide nanosheets at room temperature. The morphology and structure of the obtained material are examined by scanning electron microscopy, transition electron microscopy, X-ray diffraction and N2 adsorption–desorption. Electrochemical properties are characterized by cyclic voltammetry, galvanostatic charge–discharge and electrochemical impedance spectroscopy. An asymmetric electrochemical capacitor with high energy and power densities based on the graphene–manganese oxide hybrid material as positive electrode and graphene as negative electrode in a neutral aqueous Na2SO4 solution as electrolyte is assembled. The asymmetrical electrochemical capacitor could cycle reversibly in a voltage of 0–1.7V and give an energy density of 10.03Whkg−1 even at an average power density of 2.53kWkg−1. Moreover, the asymmetrical electrochemical capacitor exhibit excellent cycle stability, and the capacitance retention of the asymmetrical electrochemical capacitor is 69% after repeating the galvanostatic charge–discharge test at the constant current density of 2230mAg−1 for 10,000 cycles.