Disclosed are: a solid polymethylaluminoxane composition which does not utilize silica or the like, has the form of relatively fine particles, has more uniform particle sizes, and exhibits a high polymerization activity when used in the preparation of an olefin polymer; a process for producing the solid polymethylaluminoxane composition; a polymerization catalyst; and a process for producing an olefin polymer. Specifically disclosed are: a solid polymethylaluminoxane composition which has an aluminum content of 36 to 41 mass % and contains a methyl group derived from a trimethylaluminum moiety at a molar fraction of 12 mol % or less; a process for producing the solid polymethylaluminoxane composition, which comprises the step of heating an aromatic hydrocarbon solution containing polymethylaluminoxane and trimethylaluminum to cause the precipitation of the solid polymethylaluminoxane composition; a polymerization catalyst for an olefin, which comprises the solid polymethylaluminoxane composition and a transition metal compound as catalyst components; and a process for producing an olefin polymer by using the polymerization catalyst.