Nickel cobalt oxide is widely studied as the electrocapacitive material for energy storage devices because of its high electrical conductivity and multiple transition states for generating abundant Faradaic redox reactions. Constructing well-defined core/shell structures with effective charge transfer path and large surface area is one of the feasible ways to develop efficient electrocapacitive materials. This study proposes a novel insight at the first time to investigate the electrocapacitive performance of the NiCo2O4 core/shell electrodes comprising different core morphologies of one-dimensional (1D) nanowire (NW) and two-dimensional (2D) nanosheet (NS). The nickel molybdenum oxide shell synthesized on different NiCo2O4 cores shows similar morphologies, suggesting the core structure has limited influences on the growth of the shell. Simple sheet-on-wire and sheet-on-sheet configurations are therefore obtained for the core/shell structures with 1D NW and 2D NS cores, respectively. A specific capacitance (CF) of 5.53 F/cm2 is obtained at 5 mV/s for the core/shell electrode composed of the 1D NW core, along with the CF retention of 65% after 2000 cycles repeated charge/discharge process. This study provides a novel viewpoint for constructing efficient energy storage devices via carefully designing the core morphology for the core/shell structures as the electrocapacitive material.