A process for producing a highly stereospecific .alpha.-olefin polymer which comprises homopolymerizing or copolymerizing an .alpha.-olefin or copolymerizing an .alpha.-olefin with ethylene by the use of a catalyst system comprising:(A) a solid catalyst component containing a trivalent titanium compound obtained by reducing a titanium compound represented by the following general formula:Ti(OR.sup.1).sub.n X.sub.4-n (R.sup.1 represents a hydrocarbon group having 1 to 20 carbon atoms, X represents a halogen atom and n represents a number satisfying 0