An olefin polymerization catalyst comprising: (A1) a solid catalyst component prepared by contacting (a1) a dialkoxymagnesium, (b1) a tetravalent titanium halide, (c1) an electron compound, and (d1) a polysiloxane, (B) an organoaluminum compound of the formula R¹_pAlQ_3-p, and (C) an aminosilane compound of the formula (R²R³N)Si(OR⁴)₃ has a high activity to hydrogen as compared with conventional catalysts and maintains the capability of producing polymers with a high stereoregularity at a high yield.