To produce a catalyst having excellent activity in the oxidizing reaction of olefins by aq. hydrogen peroxide and excellent in double bound oxidizing electivity.

The catalyst used in the oxidizing reaction of olefins by hydrogen peroxide comprises at least one of Lewis acids represented by the formula (Rf1SO3)n1M1, [(Rf2SO2)2N]n2M2 and [Rf3SO2) 3C]n3M3 (wherein Rf1, Rf2 and Rf3 are each a 1 or more C perfluoroalkyl group, M1, M2 and M3 are each a rare earth element and n1, n2 and n3 are integer values equal to valencies of M1, M2, M3, respectively).