An olefin polymerization catalyst whose molar ratio of residual alkoxy groups to titanium is 0.60 or less, obtained by reacting (a1) an oxide of an element from Groups II to IV elements and which supports an alcohol-free halogen-containing magnesium compound, with (b1) an alcohol, at a hydroxyl group/magnesium molar ratio of 1.0 or more, then reacting that reaction mixture with (c1) a halogen-containing silicon compound, at a halogen/magnesium molar ratio of 0.20 or more, then reacting the resultant reaction mixture with (d1) an electron-donating compound, and (e) a halogen-containing titanium compound at a temperature of 120° C. to 150° C., washing the reaction mixture with an inert solvent, reacting the reaction mixture with (e) again at that temperature and washing the reaction mixture with an inert solvent, thereby providing a solid catalyst component for olefin polymerization.