Solid pmao composition and method for producing same

The present invention is a method for producing a solid PMAO composition, the method including step (a) through step (c). Step (a): an aromatic hydrocarbon solution of TMAL and PMAO including units from general formula (I) is heated, and a solid PMAO composition containing PMAO and TMAL is precipitated. At least 70% of the PMAO and TMAL in terms of aluminum precipitates. Step (b): an aromatic hydrocarbon solution of TMAL and PMAO including units represented by general formula (I) is added to a solution including the resulting solid PMAO composition. Step (c): the resulting solution is heated, and a solid PMAO composition is precipitated. At least 70% of the PMAO and TMAL in terms of aluminum precipitates. The median diameter d2 of the solid PMAO composition produced in step (c) is greater than the median diameter d1 of the solid PMAO composition produced in step (a), and the heating temperature in step (c) is the same as or different from the heating temperature in step (a). (In the formula, n represents an integer of 10-50.) According to the present invention, a high-activity solid PMAO composition is obtained even under rigorous conditions in which the grain diameter is relatively high and close to the actual reaction process. An olefin polymerization catalyst in which this solid PMAO composition is used and a method for producing an olefin polymer in which this catalyst is used are provided.