An ozone generator has a construction in which: an outer and an inner sleeves made of fused quartz or ordinary glass are mounted inside a casing of the generator, which sleeves are substantially concentrically arranged to form an air gap therebetween, while conducting films are formed on the outer periphery of the outer sleeve and the inner periphery of the inner sleeve to provide opposite discharge electrodes an inner one of which is grounded and an outer one of which is connected to high voltage side of an electric source, to which air gap a raw gas is fed while electrical discharge is conducted between these electrodes to produce ozonized gas from the raw gas.