An .alpha.-olefin polymerization catalyst system having so high a catalytic activity and stereoregularity that the catalyst residue and amorphous polymer need not be removed and a process for producing an.alpha.-olefin polymer using the catalyst system, said catalyst system consisting essentially of:(A) a trivalent titanium compound-containing solid catalyst component prepared by reducing a titanium compound, represented by the general formula Ti(OR.sup.1).sub.a X.sub.4-a in which R.sup.1 represents a hydrocarbon group having 1 to 20 carbon atoms; X represents a halogen atom; and a represents a numeral satisfying 0