Copper oxide nanoparticles were synthesized using an eco-friendly, simple and cost effective green synthesis method mediated by maize (Zea mays L.) fresh husk extract. Pure reddish cubic Cu2O nanoparticles were obtained for the first time via this green synthesis route. The Cu2O nanoparticles were thermally oxidized to pure monoclinic CuO nanoparticles at 600 °C. The phases of the copper oxides were confirmed from the X-ray diffraction (XRD) studies. The calculated crystal sizes are 39.2, 20.0 and 22.5 nm for the un-annealed, 300 °C and 600 °C annealed copper oxide nanoparticles, respectively. The values of the bandgap energies obtained from diffuse reflectance of the nanoparticles are 1.95, 1.30 and 1.40 eV, respectively, for the unannealed, 300 °C, and 600 °C annealed copper oxide nanoparticles. The electrochemical properties were studied using cyclic voltammetry (CV), galvanostatic charge discharge (GCD) cycles and electrochemical impedance spectroscopy (EIS). The unannealed reddish Cu2O nanoparticles are very stable after 2500 GCD cycles and gave the highest specific capacitance of 252 F g−1 at a scan rate of 5 mV s−1. This shows that the reddish Cu2O nanoparticle is a promising material for electrochemical energy storage applications. An asymmetric device made using activated carbon anode and unannealed copper oxide as cathode gave a specific capacitance of 87 F g−1 at a current density of 0.125 A g−1 and high energy density of 39.3 Wh kg−1 at a power density of 737.0 W kg−1.