A 3D hierarchical porous composite structure is developed via the controlled electrodeposition of a polyaniline nanofiber sponge (PANI-NFS) that fills the pores of a chemical vapor deposited graphene foam (GF). The PANI-NFS/GF composite combines the efficient electronic transport in the GF scaffold (with 100–500 μm pore size) with the rapid diffusion of the electrolyte ions into the high-specific-surface-area and densely-packed PANI-NFS (with 100–500 nm pore size). The factor of 1000 in the pore hierarchy and the synergy between the materials, that form a supercapacitor composite electrode with an integrated extended current collector, lead to both very high gravimetric and volumetric capacitances. In particular, values of 1474 F g−1 and 86 F cm−3 for a GF filling factor of 11% (leading to an estimated value of 782 F cm−3 for 100%), respectively, are obtained at a current density of 0.47 A g−1. Moreover, the composite electrode presents a capacitance retention of 83% after 15000 cycles. This excellent behavior makes the PANI-NFS/GF composite electrodes very attractive for high-performance supercapacitors.