The olefin polymerization catalyst of the invention is formed from a Group IVB transition metal compound represented by the following formula (I) and an organoaluminum oxy-compound or a compound which reacts with the transition metal compound to form an ion pair. In the olefin polymerization process of the invention using this catalyst or a catalyst formed from a Group IVB transition metal compound represented by the following formula (II) and an organoaluminum oxy-compound or a compound which reacts with the transition metal compound to form an ion pair, an olefin (co)polymer having a high molecular weight can be obtained with high polymerization activities, and besides an olefin copolymer having a high comonomer content can be obtained even if a comonomer is used in a small amount, ##STR1## wherein, M is a transition metal of Group IVB, at least one of R.sup.1 is an aryl group and the remainder is hydrogen or the like, R.sup.2 is hydrogen, an alkyl group or the like, R.sup.3 and R.sup.4 are each hydrogen, an alkyl group or the like, R.sup.6 is hydrogen, an alkyl group or the like, R.sup.7 is hydrogen, an alkyl group or the like, any one of R.sup.8 and R.sup.9 is an alkyl group, and X.sup.1 and X.sup.2 are each halogen, a hydrocarbon group or the like.