An olefin polymerization catalyst comprising (A) a solid catalyst component and (B) an organometallic compound component. The solid catalyst component (A) is prepared by a process comprising the steps of:(I) obtaining a solid (A-1) by reacting:(i) an organomagnesium component soluble in a hydrocarbon solvent and represented by the formula (M.sup.1).sub..alpha. (Mg).sub..beta. (R.sup.1).sub.p (R.sup.2).sub.q (OR.sup.3).sub.r ; and(ii) an Si--H bond-containing chlorosilane compound represented by the formula: H.sub.a SiCl.sub.b R.sup.4.sub.4-(a+b), in a ratio of from 0.01 to 100 mol (ii) per mol (i);(II) reacting the solid (A-1) with an alcohol (A-2) in a ratio of from 0.05 to 20 mol of the alcohol per mol of C--Mg bonds contained in the solid (A-1), to form a reaction product; and(III) reacting the reaction product with a titanium compound (A-4). The solid catalyst component (A) is adjusted to have an alkoxy group/titanium molar ratio of 2.4 or lower and an alkoxy group/magnesium molar ratio of 0.15 or lower.