PURPOSE: To obtain an olefin polymer having high stereoregularity with high activity, by using a catalyst component comprising a specific solid catalyst component, an organometallic compound o a metal of Group IWIII of the periodic table, and if desired, an electron donating compound.
CONSTITUTION: A dialkoxymagnesium of the formula (wherein R 1 is a hydrocarbon group), a tetraalkoxysilane, and if desired, a tetraalkoxytitanium are reacted to obtain a solid product. The resulting solid product is reacted with TiCl 4 and an aromatic carboxylic acid ester. After separation of the product, it is further reacted with TiCl 4 and an aromatic carboxylic acid ester, and washed with an aromatic hydrocarbon to obtain a solid catalyst component (a) which contains Mg, Ti, halogen and an electron donating compound as essential components and 20W80wt.% of the Ti compound of which are soluble in boiling n-heptane. Then, the component (a), an organometallic compound (b) of a metal of Group IWIII of the periodic table (e.g., triethylaluminum), and if desired, and electron donating compound (c) (e.g., an aromatic carboxylic acid ester) are blended in a molar ratio of Ti of the component (a)/the metal of the component (b)/the component (c) of 1/3W500/0W100 to obtain a catalyst. An olefin is polymerized using this catalyst.