Process for producing an oxirane compound includes treating with hydrogen peroxide in the presence of either an olefin oxidation catalyst prepared from an organic compound or a polymer compound of formula (1) ##STR00001## a tungstic acid compound, a phosphoric acid, hydrogen peroxide and a quaternary ammonium salt of formula (2) or (3) ##STR00002## or an olefin oxidation catalyst prepared from an organic compound or a polymer compound of formula (1), a tungsten compound and a quaternary ammonium salt of formula (2) or (3). The process is useful especially industrially.