Graphene (Gr)/metal oxide nanocomposites, as advanced electrode materials, have drawn significant attention in supercapacitors due to their two components' synergistic cooperation, which compensates each other's drawbacks and hence perform better than their individual components. In this study, two graphene/metal oxide nanocomposites, Gr/NiO and Gr/Co3O4 binaries were separately synthesized by a co-precipitation method in which NiO or Co3O4 as interlayer spacers were inserted into the graphene structure. The as-synthesized electroactive materials were drop-cast on the as-grown Cu(OH)2 nanowire arrays/Cu substrates fabricated by drenching copper into a rich-alkaline solution. Three-electrode's electrochemical characterizations in 6 M KOH electrolyte showed that Gr/Co3O4 and Gr/NiO exhibit high capacitances of 342.6 and 652 F g−1 at the scan sweep of 5 mV s−1, and 278.5 and 667.58 F g−1 at the current density of 1 A g−1, respectively. In addition, the power density of 250 W kg−1 leads to the energy densities of 23.17 and 9.7 Wh kg−1 for Gr/NiO and Gr/Co3O4, respectively. The Gr/NiO with the cyclic stability of 95% has a better electrochemical performance than Gr/Co3O4 (with the cyclic stability of 83%), implying more pseudocapacitance contribution of the NiO nanoparticles embedded within the graphene nanosheets and more efficient synergistic cooperation between these two components. Furthermore, full Gr/NiO/Cu(OH)2/Cu||Gr/NiO/Cu(OH)2/Cu and Gr/Co3O4/Cu(OH)2/Cu||Gr/Co3O4/Cu(OH)2/Cu symmetric cells in the organic electrolyte of 1 M TEA-BF4 in acetonitrile within the potential window of 2 V were also assembled and at 10 mV s−1, exhibited the highest specific capacitances of 32.67 and 24.86 F g−1, respectively.