A production method for an olefin-based polymer, comprising polymerizing an olefin raw material using the following components to in presence of at least one or more kinds of the following component in the olefin raw material or a polymerization solvent: a transition metal compound; a boron compound capable of forming an ion pair with the component; an organoaluminum compound represented by the following general formula (VIII); an aluminoxane represented by the following general formula (i) or (ii); a nonpolymerizable unsaturated hydrocarbon: R 17 v AIJ 3-v... (VIII) wherein in the general formula (VIII), R 17 represents an alkyl group having 1 to 20 carbon atoms, J represents a hydrogen atom, an alkoxy group having 1 to 20 carbon atoms, an aryl group having 6 to 20 carbon atoms, or a halogen atom, v represents an integer of from 1 to 3, and when v represents 2 or more, R 17 's may be identical to or different from each other, provided that at least one R 17 represents an alkyl group having 1 to 20 carbon atoms; and wherein in the general formulae (i) and (ii), Ra represents an alkyl group having 1 to 20 carbon atoms, Ra's may be identical to or different from each other, and n represents an integer of from 1 to 50; wherein the transition metal compound is a double crosslinked metallocene complex represented by a formula: wherein in the formula, M represents a metal element of Groups 3 to 10 of the periodic table or the lanthanoid series, E 1 and E 2 each represent a ligand selected from a substituted cyclopentadienyl group, an indenyl group, a substituted indenyl group, a heterocyclopentadienyl group, a substituted heterocyclopentadienyl group, an amide group, a phosphide group, a hydrocarbon group, and a silicon-containing group, form a crosslinked structure via A 1 and A 2, and may be identical to or different from each other, X represents a σ-bonding ligand, and when a plurality of X's are present, the plurality of X's may be identical to or different from each other, and X may be crosslinked with any other X, E 1, E 2, or Y, Y represents a Lewis base, and when a plurality of Y's are present, the plurality of Y's may be identical to or different from each other, and Y may be crosslinked with any other Y, E 1, E 2, or X, A 1 and A 2 each represent a divalent crosslinking group for bonding two ligands, specifically a hydrocarbon group having 1 to 20 carbon atoms, a halogen-containing hydrocarbon group having 1 to 20 carbon atoms, a silicon-containing group, a germanium-containing group, a tin-containing group, -O-, -CO-, -S-, -SO 2 -, -Se-, -NR 1 -, -PR 1 -, -P R 1 -, -BR 1 -, or -AlR 1 -, wherein R 1 represents a hydrogen atom, a halogen atom, a hydrocarbon group having 1 to 20 carbon atoms, or a halogen-containing hydrocarbon group having 1 to 20 carbon atoms, and may be identical to or different from each other, q represents an integer of from 1 to 5 representing [(valence of M)-2], and r represents an integer of from 0 to 3.. a transition metal compound; a boron compound capable of forming an ion pair with the component; an organoaluminum compound represented by the following general formula (VIII); an aluminoxane represented by the following general formula (i) or (ii); a nonpolymerizable unsaturated hydrocarbon: M represents a metal element of Groups 3 to 10 of the periodic table or the lanthanoid series, E 1 and E 2 each represent a ligand selected from a substituted cyclopentadienyl group, an indenyl group, a substituted indenyl group, a heterocyclopentadienyl group, a substituted heterocyclopentadienyl group, an amide group, a phosphide group, a hydrocarbon group, and a silicon-containing group, form a crosslinked structure via A 1 and A 2, and may be identical to or different from each other, X represents a σ-bonding ligand, and when a plurality of X's are present, the plurality of X's may be identical to or different from each other, and X may be crosslinked with any other X, E 1, E 2, or Y, Y represents a Lewis base, and when a plurality of Y's are present, the plurality of Y's may be identical to or different from each other, and Y may be crosslinked with any other Y, E 1, E 2, or X, A 1 and A 2 each represent a divalent crosslinking group for bonding two ligands, specifically a hydrocarbon group having 1 to 20 carbon atoms, a halogen-containing hydrocarbon group having 1 to 20 carbon atoms, a silicon-containing group, a germanium-containing group, a tin-containing group, -O-, -CO-, -S-, -SO 2 -, -Se-, -NR 1 -, -PR 1 -, -P R 1 -, -BR 1 -, or -AlR 1 -, wherein R 1 represents a hydrogen atom, a halogen atom, a hydrocarbon group having 1 to 20 carbon atoms, or a halogen-containing hydrocarbon group having 1 to 20 carbon atoms, and may be identical to or different from each other, q represents an integer of from 1 to 5 representing [(valence of M)-2], and r represents an integer of from 0 to 3..