A process for producing an olefin-based copolymer, which comprises copolymerizing at least one olefin selected from the group consisting of ethylene and straight chain .alpha.-olefins, and a vinyl compound (I) and a polyene (II) described below:Vinyl compound (I); a vinyl compound represented by the general formula CH.sub.2.dbd.CH--R, wherein the substituent R is a saturated hydrocarbon group and steric parameters Es and B1 of the substituent R are respectively -1.64 or less and 1.53 or more; andPolyene (II); a compound having two or more of ethylene bonds and at least one combination of two ethylene bonds in which those are bonded to each other through at least three carbon atoms.