A process for producing an epoxide represented by general formula (1a) or (1b), which comprises reacting an olefin represented by general formula (2) with a compound containing iodine and an acyloxy ion and treating the reaction product under a basic condition so as to form an oxirane ring on the stereochemically crowded side of the feed olefin. In formulae (1a), (1b) and (2), R¹, R², R³ and R⁴ represent each hydrogen, alkyl, alkenyl, aryl, alkoxy, aryloxy, acyl, alkoxycarbonyl, aryloxycarbonyl, aralkyl, silyl or silyloxy, provided that when each of these groups represents a divalent group, they may be combined together to represent a cyclic group, and that these groups may be the same or different from one another and further may be substituted or branched. The plane formed by the double bond, R¹, R², R³ and R⁴ has one side which is stereochemically more crowded than the other side.