Disclosed is a novel ethylene copolymer by copolymerizing an ethylene and at least one comonomer selected from a compound represented by the formula H.sub.2C.dbd.CHR wherein R is an alkyl group or an aryl group, and a diene, by slurry polymerization process in the presence of a solid catalyst system comprising a support, a transition metal compound and an activator capable of converting the transition metal compound into a catalytically active transition metal complex.