A novel high birefringent polymer terahertz (THz) fiber with a suspended elliptical core is proposed in this paper. The introduction of an elliptical core can enhance asymmetry to realize high mode birefringence, and a large porous outer cladding effectively isolates the core-guided mode from interacting with the surrounding environment. A full-vector finite element method(FEM) is used to analyze the characteristics of the THz fiber. Simulation results show that the suspended elliptical fiber exhibits high mode birefringence on a level of $10^{-2}$ over a wide frequency range, and an extremely large mode birefringence(${approx}0.06226$) is obtained when ellipticity is 0.2. Moreover, a suspended hollow elliptical core fiber is also discussed for the purpose of lower loss, however high mode birefringence and low relative absorption loss can not coexist in such a kind of fiber.