We introduce a continuous one-parameter family of elliptic sine-Gordon equations (SGE) characterized by the modulus 0 ≤ m ≤ 1 of Jacobi elliptic functions and analyze some of its properties and obtain its kink solution for various values of modulus m. These elliptic SGE have the novel property that while in the limit m = 0 they go over to the integrable sine-Gordon equation, in the m = 1 limit they go over to the integrable sine hyperbolic-Gordon equations (SHGE).