An olefin polymerization catalyst comprising: (A) a solid catalyst component prepared by contacting (a) a dialkoxyl magnesium, (b) a tetra-valent titanium halide, and (c) a phthalic acid diester in (d) an aromatic hydrocarbon having a boiling point in the range of 50 to 150 C., (B) an organoaluminum compound of the formula R¹_pAlQ_3-p, one or more compounds selected from the group consisting of (C) one or more halogen-containing organosilicon compounds selected from (C¹) a halogen-containing organosilicon compound of the formula R²₁Si(OR³)_4-l-mX_m and (C²) a halogen-containing organosilicon compound of the formula R⁴_qSi(OR⁵)_4-q, and (D) an organosilicon compound of the formula R⁶_sSi(OR⁷)_4-s. The catalyst exhibits excellent activity to hydrogen and the same catalytic activity and yield performance as conventional catalysts, and possesses the capability of producing polymers with stereoregularity equivalent to conventional catalysts.