A process for polymerizing an olefin comprising polymerizing or copolymerizing an olefin at a polymerization reaction temperature of 50 to 200 °C in the presence of an olefin polymerization catalyst comprising: a transition metal compound represented by the following formula, (B-1) a compound having a reduction ability which reacts with the transition metal compound to convert an imine structure moiety to a metal amide structure, and (B-2) a compound which reacts with the transition metal compound to form an ion pair; wherein M is a transition metal atom of Groups 3 to 11 of the periodic table, m is an integer of 1 to 6, Y is an oxygen atom, a sulfur atom or a selenium atom, or a nitrogen atom having a substituent R 7, R 1 to R 7 may be the same or different, they are each a hydrogen atom, a halogen atom, a hydrocarbon group, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, a sulfur-containing group, a phosphorus-containing group, a heterocyclic compound residual group, a silicon-containing group, a germanium-containing group or a tin-containing group, two or more of them may be bonded to each other to form a ring except for the case where R 1 and R 5 or R 1 and R 6 are bonded to each other to form an aromatic ring, and when m is 2 or greater, one group of R 1 to R 7 contained in one ligand and one group of R 1 to R 7 contained in other ligands may be bonded, and R 1 s, R 2 s, R 3 s, R 4 s, R 5 s, R 6 s and R 7 s may be the same or different, n is a number satisfying a valence of M, and X is a hydrogen atom, a halogen atom, a hydrocarbon group, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, a sulfur-containing group, a phosphorus-containing group, a halogen-containing group, an aluminum-containing group, a heterocyclic compound residual group, a silicon-containing group, a germanium-containing group or a tin-containing group, and when n is 2 or greater, plural groups indicated by X may be the same or different, and plural groups indicated by X may be bonded to each other to form a ring. a transition metal compound represented by the following formula, (B-1) a compound having a reduction ability which reacts with the transition metal compound to convert an imine structure moiety to a metal amide structure, and (B-2) a compound which reacts with the transition metal compound to form an ion pair; wherein M is a transition metal atom of Groups 3 to 11 of the periodic table, m is an integer of 1 to 6, Y is an oxygen atom, a sulfur atom or a selenium atom, or a nitrogen atom having a substituent R 7, R 1 to R 7 may be the same or different, they are each a hydrogen atom, a halogen atom, a hydrocarbon group, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, a sulfur-containing group, a phosphorus-containing group, a heterocyclic compound residual group, a silicon-containing group, a germanium-containing group or a tin-containing group, two or more of them may be bonded to each other to form a ring except for the case where R 1 and R 5 or R 1 and R 6 are bonded to each other to form an aromatic ring, and when m is 2 or greater, one group of R 1 to R 7 contained in one ligand and one group of R 1 to R 7 contained in other ligands may be bonded, and R 1 s, R 2 s, R 3 s, R 4 s, R 5 s, R 6 s and R 7 s may be the same or different, n is a number satisfying a valence of M, and X is a hydrogen atom, a halogen atom, a hydrocarbon group, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, a sulfur-containing group, a phosphorus-containing group, a halogen-containing group, an aluminum-containing group, a heterocyclic compound residual group, a silicon-containing group, a germanium-containing group or a tin-containing group, and when n is 2 or greater, plural groups indicated by X may be the same or different, and plural groups indicated by X may be bonded to each other to form a ring. wherein M is a transition metal atom of Groups 3 to 11 of the periodic table, m is an integer of 1 to 6, Y is an oxygen atom, a sulfur atom or a selenium atom, or a nitrogen atom having a substituent R 7, R 1 to R 7 may be the same or different, they are each a hydrogen atom, a halogen atom, a hydrocarbon group, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, a sulfur-containing group, a phosphorus-containing group, a heterocyclic compound residual group, a silicon-containing group, a germanium-containing group or a tin-containing group, two or more of them may be bonded to each other to form a ring except for the case where R 1 and R 5 or R 1 and R 6 are bonded to each other to form an aromatic ring, and when m is 2 or greater, one group of R 1 to R 7 contained in one ligand and one group of R 1 to R 7 contained in other ligands may be bonded, and R 1 s, R 2 s, R 3 s, R 4 s, R 5 s, R 6 s and R 7 s may be the same or different, n is a number satisfying a valence of M, and X is a hydrogen atom, a halogen atom, a hydrocarbon group, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, a sulfur-containing group, a phosphorus-containing group, a halogen-containing group, an aluminum-containing group, a heterocyclic compound residual group, a silicon-containing group, a germanium-containing group or a tin-containing group, and when n is 2 or greater, plural groups indicated by X may be the same or different, and plural groups indicated by X may be bonded to each other to form a ring.