Fibers with high birefringence and low loss offer notable benefits in the areas of sensing, communication, and polarization filtering. An asymmetry subwavelength suspended-core terahertz (THz) fiber composed of rectangular and arc-shaped dielectric layers is studied. Simulation results show that the fiber has both ultra-high birefringence and low loss characteristics. The birefringence value is higher than 0.038 from 0.8 to 1.0 THz, and the transmission losses of two polarization modes are lower than 0.5247 dB/cm when the thicknesses of all dielectric layers are the same. We note that the birefringence value can be further increased by adjusting the thickness of the rectangular dielectric layer. The birefringence value reaches the order of 10−1 in the frequency range of 0.82 to 1.98 THz. At 0.82 THz, the losses for x- and y-polarization modes are 0.3705 and 0.0754 dB/cm, respectively. Therefore, this type of fiber will be of great significance in eliminating the adverse influences of polarization effects in THz systems.