Abstract: An ethylene/&agr;-olefin copolymer of a weight-average molecular weight of not less than 40000 is produced by copolymerization of ethylene with an &agr;-olefin having three or more carbons by use of an olefin polymerization catalyst at a polymerization temperature of not lower than 120° C., the olefin polymerization catalyst comprising, as constitutional components, a) a metallocene compound, b) an ionizing ionic compound, and c) an organoaluminum compound, the ionizing ionic compound (b) being a compound which is capable of changing the metallocene compound (a) into a cationic form and does not further react the cationic form of the metallocene compound. This process produces an ethylene/&agr;-olefin copolymer of high molecular weight in high efficiency.