The present invention relates to a catalyst for polymerization of a conjugated diene or the like, which is composed of a metallocene-type cation complex of a gadolinium compound. Examples of such catalyst include a metallocene-type cation complex of a trivalent gadolinium compound represented by the general formula (I): R.sub.aGdX.sub.b (wherein, Gd represents gadolinium; R represents a cyclopentadienyl group, a substituted cyclopentadienyl group, an indenyl group, a substituted indenyl group, a fluorenyl group, or a substituted fluorenyl group; X represents an anion; "a" represents an integer of 1 or 2; and "b" represents an integer of 1 or 2). The present invention provides a catalyst by which polymerization of a conjugated diene or copolymerization of a conjugated diene and an aromatic vinyl compound can be carried out efficiently and inexpensively.