The present invention relates to a long-chain branched elastic terpolymer capable of satisfying excellent processability and elasticity (flexibility) at the same time, which is obtained in the presence of a Group IV transition metal catalyst, and a preparation method thereof. The elastic terpolymer is a copolymer of ethylene, an alpha-olefin having 3 to 20 carbon atoms, and a diene, wherein i) its weight average molecular weight measured by GPC is 100,000 to 500,000, and ii) x which is the ethylene content (% by weight) and y which is the density value (g/cm3) of the copolymer measured when the ethylene content is X satisfy a relationship of 0.0000175214x(x−75.65420571)+0.875≦y≦0.0000175214x(x−75.65420571)+0.881.