Supercapacitors with transition bimetallic oxides as pseudocapacitive materials have been of wide concern for their excellent energy storage performance. In this work, a simple coprecipitation method was used to synthesize the precursor, followed by calcination to prepare Ni-Cu bimetallic oxide materials. The structure, morphology and properties of the materials prepared by different precipitating agents and different calcination temperatures of NCO-H2C2O4 precursor were investigated. The optimum precipitant was determined to be H2C2O4, and Ni-Cu nanoparticles with regular lamellar microstructure were obtained at the calcination temperature of 400 °C. The nanostructure and morphology provide a large active channel for the rapid diffusion of electrolyte ions, and the specific capacitance of NCO-H2C2O4-400 electrode material can reach 740.31 F/g Cs at 1 A/g. The investigation of charge storage mechanism shows that the contribution rate of capacitance and diffusion control is about 37.9% and 67.2%, respectively. The electrochemical test results of the asymmetric supercapacitors (ASC) constructed with NCO-H2C2O4-400 and activated carbon show that the specific capacitance, energy density, and power density of the capacitor are 52.66 F/g, 16.45 Wh/kg, and 759.51 W/kg, respectively. Even after 5000 charge/discharge cycles at 5 A/g, it can still keep 90.57% of its initial capacity. This work not only provides competitive electrode materials for energy storage devices but also provides a feasible strategy for producing complex transition metal oxide materials with high capacitance performance.