PURPOSE: To produce a highly stereoregular polyolefin in good yield per unit catalyst, by using a titanium catalyst component prepared by treating a magnesium halide as a support in the presence of oxygen and impregnating the treated support with a titanium halide.

CONSTITUTION: A magnesium halide (e.g., anhydrous magnesium chloride) is ground in the presence of air or oxygen treated with a dehydrating agent such as molecular sieve and contacted with oxygen. The obtained magnesium halide (a support) and , if necessary, an oxygen-containing compound (e.g., carboxylate ester) are pulverized and brought into contact with a liquid titanium halide (e.g., titanium tetrahalide) to form a supported titanium catalyst component. An α- olefin is polymerized by using a catalyst comprising the above titanium catalyst component and an organoaluminum compound (e.g., diethylaluminum chloride).