A method for producing an α-olefin polymer, comprising the step of polymerizing one or more kinds of α-olefins each having 3 to 30 carbon atoms with a polymerization catalyst obtained by using: a metallocene compound; an ionic compound capable of reacting with the metallocene compound to transform the compound into a cation; an organometallic compound; and one or more kinds of compounds selected from the group consisting of (d-1) an alcohol, and (d-2) a phenol, the catalyst having a ratio between the component and the component of from 10:1 to 1:100 in terms of a molar ratio, and having a ratio of the component to the component of less than 1 in terms of a molar ratio, wherein the metallocene compound is a two-crosslinked metallocene compound represented by the following general formula: wherein R a and R b each independently represent a linking group represented by the following general formula -[L(R 1)(R 2)] n -, X 1 and X 2 each independently represent a hydrogen atom, a halogen atom, a hydrocarbon group having 1 to 20 carbon atoms, or an organic group having 1 to 20 carbon atoms, the organic group containing one or more kinds of atoms selected from a halogen atom, a silicon atom, an oxygen atom, a sulfur atom, a nitrogen atom, and a phosphorus atom, M represents a transition metal belonging to any one of Groups 4 to 6 of the periodic table, n represents an integer of from 1 to 3, R 1 and R 2 each independently represent 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 L represents an atom belonging to Group 14 of the periodic table, wherein the polymerization catalyst is prepared by performing a first step of mixing at least the metallocene compound and the organometallic compound, and a second step of mixing at least a mixture obtained in the first step and the component in this order. a metallocene compound; an ionic compound capable of reacting with the metallocene compound to transform the compound into a cation; an organometallic compound; and one or more kinds of compounds selected from the group consisting of (d-1) an alcohol, and (d-2) a phenol, the catalyst having a ratio between the component and the component of from 10:1 to 1:100 in terms of a molar ratio, and having a ratio of the component to the component of less than 1 in terms of a molar ratio, wherein the metallocene compound is a two-crosslinked metallocene compound represented by the following general formula: wherein R a and R b each independently represent a linking group represented by the following general formula -[L(R 1)(R 2)] n -, X 1 and X 2 each independently represent a hydrogen atom, a halogen atom, a hydrocarbon group having 1 to 20 carbon atoms, or an organic group having 1 to 20 carbon atoms, the organic group containing one or more kinds of atoms selected from a halogen atom, a silicon atom, an oxygen atom, a sulfur atom, a nitrogen atom, and a phosphorus atom, M represents a transition metal belonging to any one of Groups 4 to 6 of the periodic table, n represents an integer of from 1 to 3, R 1 and R 2 each independently represent 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 L represents an atom belonging to Group 14 of the periodic table, wherein the polymerization catalyst is prepared by performing a first step of mixing at least the metallocene compound and the organometallic compound, and a second step of mixing at least a mixture obtained in the first step and the component in this order. R a and R b each independently represent a linking group represented by the following general formula -[L(R 1)(R 2)] n -, X 1 and X 2 each independently represent a hydrogen atom, a halogen atom, a hydrocarbon group having 1 to 20 carbon atoms, or an organic group having 1 to 20 carbon atoms, the organic group containing one or more kinds of atoms selected from a halogen atom, a silicon atom, an oxygen atom, a sulfur atom, a nitrogen atom, and a phosphorus atom, M represents a transition metal belonging to any one of Groups 4 to 6 of the periodic table, n represents an integer of from 1 to 3, R 1 and R 2 each independently represent 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 L represents an atom belonging to Group 14 of the periodic table,