A catalyst for olefin polymerization comprising (A) a solid catalyst component which is prepared by causing (a) a magnesium compound, (b) a tetravalent titanium halide compound, and (c) an electron donor compound to come in contact with each other, (B) an organoaluminum compound of the formula R.sup.1.sub.pAlQ.sub.3-p, and (C) an organosilicon compound of the formula SiR.sup.2R.sup.3(OR.sup.4)(OR.sup.5), and (D) an organosilicon compound of the formula R.sup.6.sub.xSi(OR.sup.7).sub.4-x exhibits a higher hydrogen activity than conventional catalysts.