Disclosed is a catalyst component for polymerization of an olefin, which consists essentially of a contact reaction product of (A) a solid composition obtained by mixing and contacting a precipitating agent with a contact reaction product between a magnesium dihalide and a titanium tetraalkoxide and/or a polymer thereof, the addition of the precipitating agent being carried out with stirring at a stirring intensity lower than a level (2nf) two times the floatation limit stirring intensity (nf) of the reaction system, with (B) a liquid titanium compound and/or a halogen compound of silicon.This catalyst component has a high activity and provides a polymer in which the particle size is relatively large and the particle size distribution is sharply controlled.