A method for block copolymerization of a conjugated diene and an aromatic vinyl compound, which comprises the steps of carrying out homopolymerization of the conjugated diene in the presence of a catalyst composition comprising the following components: (A) a metallocene type complex of a rare earth metal compound, and (B) an ionic compound composed of a non-coordinate anion and a cation and/or an aluminoxane, and then adding the aromatic vinyl compound, and a catalyst composition for polymerization of a conjugated diene or copolymerization of a conjugated diene and an aromatic vinyl compound, which comprises the following components: (D) a neodymium complex, and (B) an ionic compound composed of a non-coordinate anion and a cation and/or an aluminoxane.