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: (A) a metallocene-type complex of a rare earth metal compound (samarium complex etc.), and (B) an ionic compound composed of a non-coordinate anion and a cation (triphenylcarbonium tetrakis(pentafluorophenyl)borate etc.) and/or an aluminoxane. The catalyst composition is useful for producing a polymer having a high cis-1,4-configuration content in the microstructure and a narrow molecular weight distribution.