An ozone generator comprises a pair of spaced opposing electrodes, electrically conductive members connecting the pair of electrodes to a high-voltage alternating-current power source to generate an electric discharge between the electrodes, a dielectric provided between the opposing electrodes, and a gas flow passage for effecting flow of a material gas defined by the surfaces of the electrodes. At least one of the surfaces of the pair of electrodes has a plurality of parallel grooves. The material gas flows in a space between the plurality of grooves and the dielectric, in a direction transverse to the grooves.