A solid polymethylaluminoxane composition is provided having uniform particle diameter in the form of fine particles of less than 5 μm employed to polymerize olefins with high polymerization activity without silica. A method for manufacturing thereof, a polymerization catalyst, and a method for manufacturing a polyolefin are also provided. The solid polymethylaluminoxane composition: has an aluminum content within a range of 36 mass % to 43 mass %; has a mole fraction of methyl groups derived from trimethylaluminum moieties relative to the total number of mols of methyl groups of 12 mol % or less; and is particulate having a median diameter based on volume within a range of 0.1 μm to less than 5 μm. In a step of heating an aromatic hydrocarbon solution containing trimethylaluminum and the polymethylaluminoxane to cause solid polymethylaluminoxane composition to precipitate, prior to or during the heat treating step, a dry, inert gas is bubbled through.