Abstract: Olefin polymers are produced by a process which comprises homopolymerizing or copolymerizing olefins in the presence of a catalyst system comprising:(A) a solid catalyst component containing a trivalent titanium compound, which is obtained by reducing a titanium compound represented by the general formula Ti(OR.sup.1).sub.n X.sub.4-n (wherein R.sup.1 is a hydrocarbon group having 1 to 20 carbon atoms, X is a halogen atom and n is a number satisfying 0<n.ltoreq.4) with an organo magnesium compound and then treating the resulting solid product with a mixture of an ether compound and titanium tetrachloride, and(B) an organo aluminum compound.The above-mentioned reducing of a titanium compound with an organo magnesium compound may be performed in the presence of an organo silicon compound having Si-O bonds.