There are disclosed a catalyst for the polymerization of an olefin which comprises (A) a transition metal complex compound represented by the general formula (I) ##STR1## wherein the respective symbols are as defined in the specification, (B) a Lewis acid and/or an ionic compound capable of reacting with the transition metal complex compound of the component (A) or its derivative to form an ionic complex, and (C) an organic aluminum compound, and a process for preparing an olefin polymer in the presence of this catalyst. The catalyst of the present invention is inexpensive and has a high activity, and according to the present invention, the deterioration of the activity can be inhibited and the molecular weight of the obtained polymer can be easily adjusted, so that the olefin polymer can efficiently be prepared which has an optional molecular weight and can possess a molecular weight distribution in which low-molecular weight and high-molecular weight portions decrease.