A method for producing an olefin polymer, which comprises polymerizing or copolymerizing olefins in the presence of a catalyst comprising:(A) a solid catalyst component obtained by thermally reacting (a.sub.1) a magnesium compound of the formula Mg(OR.sup.1).sub.n (OR.sup.2).sub.2-n wherein each of R.sup.1 and R.sup.2 which may be the same or different is an alkyl group, an aryl group or an aralkyl group, and n is 2.gtoreq.n.gtoreq.0, (a.sub.2) a titanium compound of the formula Ti(OR.sup.3).sub.4 wherein R.sup.3 is an alkyl group, an aryl group or an aralkyl group and (a.sub.3) a silicon compound of the formula Si(OR.sup.4).sub.4 wherein R.sup.4 is an alkyl group, an aryl group or an aralkyl group and contacting and treating (a) the resulting thermal reaction product with (b) a halogen-containing titanium compound and (c) an electron donative compound, and(B) an organometallic compound of a metal of Groups I-III of the Periodic Table.