A carrier for carrying an osmium oxide comprising an aromatic polyolefin polymer having a group shown by the general formula [1] as a substituent on the aromatic ring of said polyolefin polymer: --A'--O(--A--O).sub.n--R[1] (wherein A is an alkylene group; A' is a direct link or an alkylene group; R is an aryl group; and n is an integer of 1 to 10), an osmium oxide carried by the carrier for carrying an osmium oxide and a method for producing the osmium oxide carried by said carrier are disclosed. Since the osmium oxide carried by the carrier of the present invention has a hydrophilic group, in an oxidation reaction and an asymmetric oxidation reaction, particularly in a heterogeneous solvent system, the osmium oxide carried by the carrier of the present invention enables to produce a diol compound easily and in a high optical yield.