A method for producing a high-activity solid PMAO composition is provided, involving: (a) heating an aromatic hydrocarbon solution of TMAL and PMAO containing units having formula (I), and precipitating a solid PMAO composition containing PMAO and TMAL; (b) adding an aromatic hydrocarbon solution of TMAL and PMAO containing units represented by formula (I) to a solution containing the solid PMAO composition; and (c) heating the resulting solution, thereby precipitating a solid PMAO composition. In steps (b) and (c), at least 70% of the PMAO and TMAL in terms of aluminum precipitates. The median diameter d2 of the solid PMAO composition produced in (c) is greater than the median diameter d1 of the solid PMAO composition produced in (a). -[(Me)AlO]n—  (I) In formula (I), n represents an integer of 10-50. An olefin polymerization catalyst using the solid PMAO composition and a method for producing an olefin polymer using this catalyst are also described.