Method for producing copolymer

A method for producing a copolymer characterized by comprising a step of polymerizing a conjugated diene compound and an olefin in the presence of a polymerization catalyst composition comprising at least one complex selected from the group consisting of a metallocene complex represented by the following general formula (II):

• wherein M in the general formula (II) is a lanthanoid element, scandium or yttrium, and CpR in the general formula (II) is independently a non-substituted or substituted indenyl, and X′ in the general formula (II) is a hydrogen atom, a halogen atom, an alkoxide group, a thiolate group, an amide group, a silyl group or a hydrocarbon group having a carbon number of 1-20, and L in the general formula (II) is a neutral Lewis base, and w in the general formula (II) is an integer of 0-3),
• and a half-metallocene cation complex represented by the following general formula (III):
• wherein M in the general formula (III) is a lanthanoid element, scandium or yttrium, and CpR′ in the general formula (III) is a non-substituted or substituted cyclopentadienyl, indenyl or fluorenyl, and X in the general formula (III) is a hydrogen atom, a halogen atom, an alkoxide group, a thiolate group, an amide group, a silyl group or a hydrocarbon group having a carbon number of 1-20, and L in the general formula (III) is a neutral Lewis base, and w in the general formula (III) is an integer of 0-3, and [B]− in the general formula (III) is a non-coordinating anion, and
• wherein the cis-1,4 bond content of the conjugated diene compound portion in the copolymer is not less than 85%.