PURPOSE: A catalytic component having a high activity and providing polymers with good properties, prepared by contacting a silicon halide with a solid composition consisting of a magnesium dihalide, a titanium tetraalkoxide and a polymeric silicon compound.

CONSTITUTION: A catalytic component for olefin polymerization, which is a product prepared by contacting a silicon halide (e.g., SiCl4) with a solid composition consisting of a magnesium dihalide (e.g., MgCl2), a titanium tetraalkoxide [e.g., Ti(OC2H5)4] and a polymeric silicon compound of the formula, wherein R is a hydrocarbon residue, e.g., methylhydrogenpolysiloxane. It is possible to produce a polymer with good properties in high activity by polymerizing an α-olefin with the aid of a Ziegler catalyst having the solid catalytic component as a transition metal component.