According to the present invention, there is provided a catalyst component of metal oxide support type which has a high catalytic activity, that is, a little catalyst residue in a polymer, as well as improved catalytic grain strength sufficient for practical use and which hardly deteriorates even after storage for a long time. The catalyst component is obtained by contacting(a) a metal oxide with(b) a dihydrocarbyl magnesium, then contacting the resulting composition with(c) a compound represented by the general formula X.sup.1 .sub.n M(OR.sup.1).sub.m-n wherein X.sup.1 is a hydrogen atom, halogen atom or a hydrocarbon group of 1 to 20 carbon atoms, M is a boron, carbon, aluminum, silicon or phosphorus atom, R.sup.1 is a hydrocarbon group of 1 to 20 carbon atoms, m is the atomic valence of M and m>n.gtoreq.0, and(d) a titanium alkoxide represented by the general formula Ti(OR.sup.2).sub.4 wherein R.sup.2 is a hydrocarbon group of 1 to 12 carbon atoms, and then contacting the resulting solid with (e) an olefin in the presence of (f) an organoaluminum compound, then with (g) a halogen-containing alcohol and further with (h) an electron donating compound and (i) a titanium compound.