A solid catalyst component for polymerization of olefins prepared by contacting (a) a dialkoxy magnesium compound, (b) a tetra-valent titanium halide, and (c) an electron donor compound of the formula R.sup.1R.sup.2C(COOR.sup.3).sub.2 suspended in (d) an aromatic hydrocarbon having a boiling point in the range of 50 150.degree. C. The catalyst containing the catalyst component is excellent in the olefin polymerization catalyst activity to hydrogen and can produce a polymer with a high stereoregularity in a high yield.