This invention relates to a method for producing a copolymer of a conjugated diene compound and an unconjugated olefin other than the conjugated diene compound having a high cis-1,4 bond content of a conjugated diene compound portion, and more particularly to a method for producing a copolymer characterized by comprising a step of polymerizing a conjugated diene compound and an unconjugated olefin other than the conjugated diene compound in the presence of a polymerization catalyst composition including at least one complex selected from a metallocene complex represented by the following general formula (I): (wherein M is a lanthanoid element, scandium or yttrium, and CpR is independently a non-substituted or substituted indenyl, and Ra-Rf are independently an alkyl group having a carbon number of 1-3 or a hydrogen atom, and L is a neutral Lewis base, and w is an integer of 0-3) and so on.