Olefin polymers with a broad molecular weight distribution can be obtained while maintaining the high stereoregularity of the polymers by polymerizing olefins using a catalyst comprising (A) a solid catalyst component prepared by contacting (a) a dialkoxymagnesium, (b) a tetravalent titanium halide compound, and (c) an electron donor compound one another, (B) an organoaluminum compound of the formula R¹_pAlQ_3-p, and (C) an aminosilane compound of the formula R²R³Si(OR⁴)₂.