Abstract: A solid catalyst component containing a trivalent titanium compound, 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 of 1 to 20 carbon atoms, X is a halogen atom, and n is a number satisfying 0<n.ltoreq.4) with an organomagnesium compound in the presence of an alcohol compound and/or a phenol compound to obtain a solid product and then treating the solid product with a mixture of an ether compound and titanium tetrachloride; a catalyst system comprising:(A) said solid catalyst component, and(B) an organoaluminum compound; and a process for producing an olefin polymer, which comprises homopolymerizing an olefin or copolymerizing olefins using said catalyst system.