A polyolefin having superior particle properties such as an extremely high bulk density, a large average particle diameter and a narrow particle size distribution, and having a narrow molecular weight distribution, is obtained in high yield, by polymerizing an olefin, using a catalyst comprising a solid catalyst component and an organometallic compound, the solid catalyst component being obtained by reacting a) a silicon oxide and/or an aluminum oxide, the reaction product of an organomagnesium compound and a compound of the general formula Me(OR).sub.n X.sub.Z-n, and a titanium compound, in the presence of ROH, and further reacting the resulting reaction product with a compound of the general formula AlR.sub.q X.sub.3-q.