Combining hierarchical nickel–cobalt oxides (NCO) with cost-effective glucose-based carbons could be attractive electrode materials for high-performance supercapacitor. The bimetallic nickel (Ni) and cobalt (Co) hydroxide was directly electrodeposited for 120, 180, 300, 480, and 600 s, respectively, on a conductive Ni foam as the NCO/Ni electrodes. The (NCO/Ni)-480 electrode showed the highest capacitance among NCO/Ni electrodes. Furthermore, an asymmetric supercapacitor (ASC) was assembled by utilizing (NCO/Ni)-480 as a positive electrode and glucose-based activated-carbon coated on Ni foam, (G-AC)/Ni, as a negative electrode in solid state carboxymethyl cellulose-lithium nitrate (CMC-LiNO3) gel electrolyte. At the potential window of 1.5 V, the device exhibits a prominent energy density of 45.3 Wh kg−1 at a power density of 0.743 kW kg−1 (1 A g−1) and excellent cycling stability of 89.7% of the initial capacity retention over 10,000 cycles. The outstanding electrochemical performances of the ASC can be ascribed to the synergistic effect of hierarchical Ni–Co oxides, mesoporous G-AC, three-dimensional Ni foam collector, and binder-free preparation, which facilitates a faster diffusion of the electrolyte ion into the electrode material and provides a stronger adhesion of active materials with the current collector.