The present invention provides a process for producing an ethylene-.alpha.-olefin-unconjugated polyene random copolymer in an aliphatic hydrocarbon solvent under conditions of high-temperature and high-activity. The process comprises polymerizing at least the following components (a)-(c) in an aliphatic hydrocarbon solvent in the presence of a catalyst comprising (A) a transition metal complex having at least one cyclopentadienyl skeleton and (B) an organoaluminum compound and (C) a boron compound as co-catalysts wherein at least a part of the polyene (c) and at least a part of the boron compound (C) are previously contacted with each other before they are introduced into a polymerization reactor: (a): ethylene (b): an .alpha.-olefin of 3-20 carbon atoms (c): a polyene.