The enhancement of energy density at high power density is highly desired in design of supercapacitor, which relies on the electrochemically accessible electrode area, electrons/ions diffusion channels of electrodes and the device assembly manner. Herein, graphitized and porous fullerene carbon soot is used as matrix for preparation of activated carbon (denoted as a-FC). The high specific surface area, hierarchical pore sizes and moderate graphitization degree of a-FC enable balanced specific capacitance, rate capability and cycleability. Meanwhile, graphene-Co3O4 composite (GC) with cross-linked porous Co3O4 nanofibers array onto graphene sheet is hydrothermally deposited on Ni foam substrate. The pseudocapacitive GC electrode can offer superior capacitance (1935 F g−1 at 5 A g−1), rate capability (68% capacitance retaining ratio within 0.5–50 A g−1) and considerable cycleability (17% capacitance decline within 2000 charge-discharge cycles) comprehensively. Furthermore, the asymmetric supercapacitor based on the a-FC and GC electrodes delivers balanced energy density (50.3–20.9 Wh kg−1), power density (786–12128 W kg−1) and cycleability (77% initial capacitance maintaining ratio within 5000 charge-discharge cycles), highlighting the potential in efficient energy storage device.