Olefins are polymerized in the presence of a catalyst which comprises the combination of:[I] a solid substance obtained by the reaction of at least the following two components:(i) a magnesium compound represented by the general formula R.sup.1.sub.m (OR.sup.2).sub.n MgX.sub.2-m-n wherein R.sup.1 and R.sup.2 are each a hydrocarbon radical having 1 to 24 carbon atoms, X is a halogen atom, m is 0.ltoreq.m.ltoreq.2 and n is 0.ltoreq.n.ltoreq.2, provided 0.ltoreq.m+n.ltoreq.2, and(ii) a titanium compound and/or a vanadium compound;[II] a silicon compound represented by general formula R.sup.1 mSi(OR.sup.2).sub.n X.sub.4-m-n wherein R.sup.1 and R.sup.2 are each hydrocarbon radical having 1 to 24 carbon atoms, X is a halogen atom, m is 0.ltoreq.m