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The purpose of the present invention is to provide a method for producing a copolymer capable of obtaining at high yield a copolymer having a high cis-1, 4-bond content of the conjugated diene moiety even when a cyclic olefin compound is used as a monomer. To achieve the above purpose, the present invention is characterized by being provided with a step that polymerizes a conjugated diene compound and a cyclic olefin compound in the presence of a catalyst composition including at least one compound selected from the group consisting of rare earth element compounds represented by formula (I), ionic compounds, and halogen compounds, a compound represented by formula (II), and a coordination compound capable of serving as a ligand. M-(AQ1) (AQ2) (AQ3) ···(I) YR1aR2bR3c···(II)