A carbon cloth/gallium oxynitride has a chemical formula of GaOxNy, where x=0.1-0.3 and y=0.7-0.9; and has a N/O molar ratio of 2.3 to 9. The carbon cloth/gallium oxynitride is a composite formed by loading gallium oxynitride nanoparticles on carbon cloth fibers, wherein the gallium oxynitride nanoparticles have a size range of 10 to 70 nm, and the carbon cloth/gallium oxynitride has a discharge specific capacitance of 30 to 865 mF cm−2 at current densities ranging from 0.5 to 100 mA cm−2. The working electrode is made from the carbon cloth/gallium oxynitride; and the supercapacitor is composed of the carbon cloth/gallium oxynitride working electrodes, a separator, an electrolyte, and an outer package.