Novel 3D flower-like Co3O4-G>N-PEGm composites have been synthesized by employing a solvothermal method, in which the incorporating graphene nanosheets are modified with methoxypolyethylene glycol (mPEG) via nitrene chemistry to form 2D macromolecular brushes. In Co3O4-G>N-PEGm, the flower-like Co3O4 microspheres can anchor on the G>N-PEGm nanosheets, corresponding to the coordination bonds between the lone pair of electrons on the mPEG polymer chains of the G>N-PEGm macromolecular brushes and cobalt ions. Owing to the novel structure, a high specific capacitance value of 1625.6 F g-1 at a current density of 0.5 A g-1 can be achieved in KOH solution. Meanwhile, 3D rGO-CNT>N-PEGm aerogels (GCA), as the negative electrode of electrical double-layer capacitor materials, exhibit a high reversible specific capacitance of 313.8 F g-1 at a current density of 2 A g-1. Based on the high electrochemical performance of both electrode materials, the double ion-buffering reservoirs of asymmetric supercapacitors configured with the Co3O4-G>N-PEGm as the positive electrode and 3D GCA as the negative electrode can deliver a high energy density of 34.4 W h kg-1 at a power density of 400 kW kg-1.