A method for producing a syndiotactic a-olefin polymer comprising polymerizing one or more monomers selected from α-olefins having 2 or more carbon atoms at a temperature within the range from 0 to 170°C in the presence of a catalyst which comprises: (a-1) a bridged metallocene compound represented by the following Formula; and (b) at least one compound selected from: (b-1) an organoaluminum oxy compound, (b-2) a compound which reacts with the bridged metallocene compound (a-1) to form an ion pair, and (b-3) an organoaluminum compound; wherein each of R 1, R 2, R 3 and R 4 is a hydrogen atom; R 5, R 8, R 9 and R 12, which may be identical to or different from each other, are each selected from hydrogen, hydrocarbon group and a silicon-containing group; R 6, R 7, R 10 and R 11, which may be identical to or different from each other, are each selected from a hydrocarbon group and a silicon-containing group; in one or more pairs of adjacent groups selected from R 5 and R 6, R 7 and R 8, R 8 and R 9, R 9 and R 10, and R 11 and R 12, the adjacent groups may be linked to each other to form a ring; R 13 and R 14, which may be identical to or different from each other, are each an atom or a substituent selected from the group consisting of a hydrogen atom, a hydrocarbon group having 2 to 20 carbon atoms, and a silicon atom-containing group; M is Ti, Zr or Hf; Y is carbon; and Q, which may be identical to or different from each other, is selected from a halogen, a hydrocarbon group, an anion ligand and a neutral ligand capable of coordination with a lone electron pair; and j is an integer from 1 to 4 (a-1) a bridged metallocene compound represented by the following Formula; and (b) at least one compound selected from: (b-1) an organoaluminum oxy compound, (b-2) a compound which reacts with the bridged metallocene compound (a-1) to form an ion pair, and (b-3) an organoaluminum compound; wherein each of R 1, R 2, R 3 and R 4 is a hydrogen atom; R 5, R 8, R 9 and R 12, which may be identical to or different from each other, are each selected from hydrogen, hydrocarbon group and a silicon-containing group; R 6, R 7, R 10 and R 11, which may be identical to or different from each other, are each selected from a hydrocarbon group and a silicon-containing group; in one or more pairs of adjacent groups selected from R 5 and R 6, R 7 and R 8, R 8 and R 9, R 9 and R 10, and R 11 and R 12, the adjacent groups may be linked to each other to form a ring; R 13 and R 14, which may be identical to or different from each other, are each an atom or a substituent selected from the group consisting of a hydrogen atom, a hydrocarbon group having 2 to 20 carbon atoms, and a silicon atom-containing group; M is Ti, Zr or Hf; Y is carbon; and Q, which may be identical to or different from each other, is selected from a halogen, a hydrocarbon group, an anion ligand and a neutral ligand capable of coordination with a lone electron pair; and j is an integer from 1 to 4 (b-1) an organoaluminum oxy compound, (b-2) a compound which reacts with the bridged metallocene compound (a-1) to form an ion pair, and (b-3) an organoaluminum compound; wherein each of R 1, R 2, R 3 and R 4 is a hydrogen atom; R 5, R 8, R 9 and R 12, which may be identical to or different from each other, are each selected from hydrogen, hydrocarbon group and a silicon-containing group; R 6, R 7, R 10 and R 11, which may be identical to or different from each other, are each selected from a hydrocarbon group and a silicon-containing group; in one or more pairs of adjacent groups selected from R 5 and R 6, R 7 and R 8, R 8 and R 9, R 9 and R 10, and R 11 and R 12, the adjacent groups may be linked to each other to form a ring; R 13 and R 14, which may be identical to or different from each other, are each an atom or a substituent selected from the group consisting of a hydrogen atom, a hydrocarbon group having 2 to 20 carbon atoms, and a silicon atom-containing group; M is Ti, Zr or Hf; Y is carbon; and Q, which may be identical to or different from each other, is selected from a halogen, a hydrocarbon group, an anion ligand and a neutral ligand capable of coordination with a lone electron pair; and j is an integer from 1 to 4 R 5, R 8, R 9 and R 12, which may be identical to or different from each other, are each selected from hydrogen, hydrocarbon group and a silicon-containing group; R 6, R 7, R 10 and R 11, which may be identical to or different from each other, are each selected from a hydrocarbon group and a silicon-containing group; in one or more pairs of adjacent groups selected from R 5 and R 6, R 7 and R 8, R 8 and R 9, R 9 and R 10, and R 11 and R 12, the adjacent groups may be linked to each other to form a ring; R 13 and R 14, which may be identical to or different from each other, are each an atom or a substituent selected from the group consisting of a hydrogen atom, a hydrocarbon group having 2 to 20 carbon atoms, and a silicon atom-containing group; M is Ti, Zr or Hf; Y is carbon; and Q, which may be identical to or different from each other, is selected from a halogen, a hydrocarbon group, an anion ligand and a neutral ligand capable of coordination with a lone electron pair; and j is an integer from 1 to 4