A method for preparing a solid olefin polymerization catalyst, which comprises the steps of: producing a modified methylaluminoxane preparation, in which a mole fraction of methyl group of the aluminoxane unit with respect to a total number of moles of the hydrocarbon group having 2 to 20 carbon atoms plug methyl group present in the modified methylaluminoxane preparation is 65 mol % or greater as determined by 1 H NMR in accordance with the procedure disclosed in the description, by a method comprising the steps of: hydrolyzing an organoaluminum compound represented by the following general formula: R 1 m AlX 3-m wherein R 1 represents a straight-chained or branched hydrocarbon group selected from the group consisting of alkyl, alkenyl, and aryl groups having 2 to 20 carbon atoms; X represents a hydrogen atom, halogen atom, alkoxy group, or allyloxy group; and m is an integer such that 0 < m ≤ 3; subsequently adding trimethyl aluminum and carrying out hydrolysis in the presence of water, repeating the step of adding trimethyl aluminum and carrying out hydrolysis as many times as necessary; exposing fine particles of carrier to said modified methylaluminoxane preparation; and subsequently exposing the fine particles carrier to a transitional metal compound represented by the following general formula: MR 2 R 3 R 4 R 5 wherein M represents a transitional metal element; and R 2, R 3, R 9 and R 5 together form any organic group having a cycloalkadienyl skeleton or are each independently selected from the group consisting of an organic group having a cycloalkadienyl skeleton, alkyl group, alkoxy group, aryloxy group, alkylsilyl group, alkylamide group, alkylimide group, alkylamino group, alkylimino group, and halogen atom. producing a modified methylaluminoxane preparation, in which a mole fraction of methyl group of the aluminoxane unit with respect to a total number of moles of the hydrocarbon group having 2 to 20 carbon atoms plug methyl group present in the modified methylaluminoxane preparation is 65 mol % or greater as determined by 1 H NMR in accordance with the procedure disclosed in the description, by a method comprising the steps of: hydrolyzing an organoaluminum compound represented by the following general formula: R 1 m AlX 3-m wherein R 1 represents a straight-chained or branched hydrocarbon group selected from the group consisting of alkyl, alkenyl, and aryl groups having 2 to 20 carbon atoms; X represents a hydrogen atom, halogen atom, alkoxy group, or allyloxy group; and m is an integer such that 0 < m ≤ 3; subsequently adding trimethyl aluminum and carrying out hydrolysis in the presence of water, repeating the step of adding trimethyl aluminum and carrying out hydrolysis as many times as necessary; hydrolyzing an organoaluminum compound represented by the following general formula: R 1 m AlX 3-m wherein R 1 represents a straight-chained or branched hydrocarbon group selected from the group consisting of alkyl, alkenyl, and aryl groups having 2 to 20 carbon atoms; X represents a hydrogen atom, halogen atom, alkoxy group, or allyloxy group; and m is an integer such that 0 < m ≤ 3; subsequently adding trimethyl aluminum and carrying out hydrolysis in the presence of water, repeating the step of adding trimethyl aluminum and carrying out hydrolysis as many times as necessary; exposing fine particles of carrier to said modified methylaluminoxane preparation; and subsequently exposing the fine particles carrier to a transitional metal compound represented by the following general formula: MR 2 R 3 R 4 R 5 wherein M represents a transitional metal element; and R 2, R 3, R 9 and R 5 together form any organic group having a cycloalkadienyl skeleton or are each independently selected from the group consisting of an organic group having a cycloalkadienyl skeleton, alkyl group, alkoxy group, aryloxy group, alkylsilyl group, alkylamide group, alkylimide group, alkylamino group, alkylimino group, and halogen atom.