A method for olefin polymerization, in which essentially ethylene and optionally one or more monomers selected from alpha-olefins are polymerized in the presence of an olefin polymerization catalyst so that an ethylene based polymer with an ethylene content of more than 50 mol% is obtained, wherein the olefin polymerization catalyst comprises: a bridged metallocene compound of formula wherein Y is a carbon or silicon atom; M is Ti, Zr or Hf; R 1 to R 4 are hydrogen; R 5 to R 12, which may be the same or different, are each hydrogen, a hydrocarbon group or a silicon-containing group; neighboring substituents of R 5 to R 12 may be linked with each other to form a ring; and arbitrary three or more substituents of R 5 to R 12 are hydrocarbon groups of 1 to 20 carbon atoms or silicon-containing groups; R 6 and R 7, and R 10 and R 11 are linked with each other to form rings; R 13 and R 14, which may be the same or different, are each a hydrocarbon group or a silicon-containing group and may be linked with each other to form a ring; Q is a halogen, a hydrocarbon group, an anionic ligand or a neutral ligand capable of coordination by a lone pair of electrons, and may be the same or different when plural; and j is an integer from 1 to 4, wherein the hydrocarbon group is of 1 to 20 carbon atoms and is selected from alkyl, alkenyl, alkynl and aryl groups which consist of carbon and hydrogen; and corresponding groups to the above groups in which part of hydrogen atoms connected with carbon is substituted with a halogen atom or an oxygen-, nitrogen- or silicon-containing group, or in which arbitrary two adjacent hydrogen atoms are both substituted to form an alicyclic or aromatic ring, and at least one compound selected from: (B-1) an organometallic compound, (B-2) an organoaluminum oxy-compound and (B-3) a compound which reacts with the metallocene compound to form an ion pair. a bridged metallocene compound of formula wherein Y is a carbon or silicon atom; M is Ti, Zr or Hf; R 1 to R 4 are hydrogen; R 5 to R 12, which may be the same or different, are each hydrogen, a hydrocarbon group or a silicon-containing group; neighboring substituents of R 5 to R 12 may be linked with each other to form a ring; and arbitrary three or more substituents of R 5 to R 12 are hydrocarbon groups of 1 to 20 carbon atoms or silicon-containing groups; R 6 and R 7, and R 10 and R 11 are linked with each other to form rings; R 13 and R 14, which may be the same or different, are each a hydrocarbon group or a silicon-containing group and may be linked with each other to form a ring; Q is a halogen, a hydrocarbon group, an anionic ligand or a neutral ligand capable of coordination by a lone pair of electrons, and may be the same or different when plural; and j is an integer from 1 to 4, wherein the hydrocarbon group is of 1 to 20 carbon atoms and is selected from alkyl, alkenyl, alkynl and aryl groups which consist of carbon and hydrogen; and corresponding groups to the above groups in which part of hydrogen atoms connected with carbon is substituted with a halogen atom or an oxygen-, nitrogen- or silicon-containing group, or in which arbitrary two adjacent hydrogen atoms are both substituted to form an alicyclic or aromatic ring, and at least one compound selected from: (B-1) an organometallic compound, (B-2) an organoaluminum oxy-compound and (B-3) a compound which reacts with the metallocene compound to form an ion pair. (B-1) an organometallic compound, (B-2) an organoaluminum oxy-compound and (B-3) a compound which reacts with the metallocene compound to form an ion pair.