A catalyst comprising an organoaluminum compound and a vanadium chelate compound having the lability to cause olefins to undergo living coordination polymerization is contacted with a terminal diolefin to obtain a catalyst for living polymer production. When the above contact is:conducted in the presence of a cycloolefin or an internal olefin, the yield of a living polymer can be improved. By modifying all ends of the living polymer obtained, a telechelic olefin polymer is obtained in which all the polymer chains are modified with functional groups.