Abstract: A catalyst comprising (A) a solid catalyst component obained by reacting a homogeneous solution containing (i) at least one member selected from the group consisting of a combination of metallic magnesium and a hydroxyl organic compound, and an oxygen-containing organic compound of magnesium, (ii) an electron donor compound and (iii) an oxygen-containing organic compound of titanium with (iv) at least one aluminum halide compound and further reacting the obtained solid product with (v) an electron donor compound and (vi) a titanium halide compound, (B) at least one member selected from the group consisting of organic metal compounds of metals of the groups Ia, IIa, IIb, IIIb and IVb of the periodic table, and (C) an electron donor compound, is valuable as the catalyst for preparing a stereoregular polyolefin by homopolymerization or copolymerization of an .alpha.-olefin having at least 3 carbon atoms.