An olefin polymerization catalyst formed from (A) a solid titanium catalyst component containing magnesium, titanium and halogen as essential ingredients, (B) an organoaluminum compound, and (C) an organosilicon compound containing a cyclopentyl group, a cyclopentenyl group, a cyclopentadienyl group or a derivative derived from any of these groups.A polymerization process which comprises polymerizing or copolymerizing olefins in the presence of the olefin polymerization catalyst to form a homopolyolefin having high stereoregularity or a copolyolefin having a narrow composition distribution.