A solid titanium catalyst component (A) of a catalyst system useful in the polymerization of olefins or copolymerization of two or more olefins or one or more olefins and a diene is prepared by contacting a liquid hydrocarbon solution of (i) a magnesium compound, such as magnesium chloride, with (ii) a liquid titanium compound, such as TiCl.sub.4, or a solution of a titanium compound in a hydrocarbon solvent, to form a solid product. The solid product is formed in the presence of (D) an electron donor, e.g. methyl formate, acetic acid, acetic anhydride, acetone, methyl ether, butyl Cellosolve, dimethyl carbonate, methyl silicate. The solid product is also contacted with a polycarboxylic acid ester, e.g. diethyl methylsuccinate. The polymerization or copolymerization of the olefin is carried out in the presence of the solid titanium catalyst (A) and (B) an organometallic compound of a Group I to III metal and (C) an organic silicon compound having an Si--O--C bond. Granular or spherical polyethylene, polypropylene, poly(butene-1), poly(4-methylpentene-1), etc. are produced in high yield, with good flowability, high bulk density, and narrow particle size distribution. The polymers can be produced over a wide range of melt index values without reduction in stereospecificity. Catalyst activity is retained with passage of time.