A process for producing an olefin polymer with high polymerization activity without using an expensive co-catalyst or using a limited amount of the co-catalyst, more particularly a process for producing a high molecular weight (co)polymer with high polymerization activity even at a high polymerization temperature which is more practical.At least one olefin is polymerized by means of a polymerization catalyst comprising at least one transition metal compound selected from transition metal compounds which have a substituted indenyl group, represented by a certain specific chemical formula, and an organoaluminum compound represented by the formula Al(R).sub.3.