We attempt to meet the general design requirements for high-performance supercapacitor electrodes by combining the strategies of lightweight substrate, porous nanostructure design, and conductivity modification. We fabricate a new type of 3D porous and thin graphite foams (GF) and use as the light and conductive substrates for the growth of metal oxide core/shell nanowire arrays to form integrated electrodes. The nanowire core is Co3O4, and the shell is a composite of conducting polymer (poly(3,4-ethylenedioxythiophene), PEDOT) and metal oxide (MnO2). To show the advantage of this integrated electrode design (viz., GF + Co3O4/PEDOT-MnO2 core/shell nanowire arrays), three other different less-integrated electrodes are also prepared for comparison. Full supercapacitor devices based on the GF + Co3O4/PEDOT-MnO2 as positive electrodes exhibit the best performance compared to other three counterparts due to an optimal design of structure and a synergistic effect.