Method for producing a small 径固-shaped polymethylaluminoxane composition

The present invention, without using silica or the like, a fine particle of less than 5 [mu] m, the particle size is also more uniform, the polymerization activity is high solid polymethylaluminoxane composition in the preparation of olefin polymer and a manufacturing method thereof , to provide a method of manufacturing a polymerization catalyst and an olefin-based polymer. Method for producing a solid polymethylaluminoxane composition of the present invention, the aluminum content is in the range of 36 wt% of 43 wt%, mole fraction of methyl groups derived from trimethylaluminum sites be 12 mol% or less and a particulate, a volume-based median diameter of about solid polymethylaluminoxane composition in the range of less than 0.1 .mu.m to 5 .mu.m. In the step of heating the aromatic hydrocarbon solution containing the polymethylaluminoxane and trimethylaluminum to precipitate a solid polymethylaluminoxane composition, comprising a bubbling dry inert gas during the heating before or heat treatment.