The present invention provides: a solid polymethylaluminoxane composition which can be prepared without using silica or the like, has the form of microparticles each having a particle diameter smaller than 5 mum, has more uniform particle diameters, and can exhibit a high polymerization activity when used in the preparation of an olefin polymer; a method for producing the solid polymethylaluminoxane composition; a polymerization catalyst; and a method for producing an olefin polymer. The method for producing a solid polymethylaluminoxane composition according to the present invention relates to a solid polymethylaluminoxane composition having an aluminum content of 36 to 43 mass% and a molar fraction of a methyl group derived from a trimethylaluminum moiety of 12 mol% or less, having the form of particles, and having a volume-based median diameter of 0.1 [mu]m or larger and smaller than 5 [mu]m. In the method, a step of heating an aromatic hydrocarbon solution containing polymethylaluminoxane and trimethylaluminum to cause the solid polymethylaluminoxane composition to be precipitated involves bubbling a dried inert gas prior to or during the heating treatment.