Abstract: Disclosed is a process for the preparation of the former catalyst component of a catalyst for the polymerization of .alpha.-olefins composed of a titanium-based catalyst component and an organo aluminium compound. According to the above process, a magnesium halide is copulverized with aluminium isopropoxide to form a first copulverization product, to which an electron donor compound is added for copulverization to form a second copulverization product, and the second copulverization product is brought into contact with a titanium halide followed by washing with an inert organic solvent.In the polymerization of .alpha.-olefins by use of the former catalyst component as above, both polymerization activity per unit weight of the catalyst component and yield of stereoregular polymers are remarkably increased.