A catalyst component for an alpha-olefin polymerization catalyst (comprising an organoaluminium compound, an external electron donor and a solid catalyst component obtained by reaction of a magnesium-containing compound with a titanium halogen compound) is prepared by the steps of:
(a) precipitating a water-soluble magnesium compound from an aqueous solution thereof using an alkali; (b) separating the solid magnesium component and dissolving it in hydrochloric acid; (c) evaporating the resultant solution until dry; (d)heating the salt mixture obtained at 130 to 150°C; (e) dissolving the magnesium component in ethanol; (f) drying the ethanolic solution of the magnesium component by periodic azeotropic distillation; (g) precipitating a solid carrier component from the ethanolic solution; and (h) reacting the solid carrier component with a titanium halogen compound in the presence of an internal electron donor or without an electron donor.