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Two highly birefringent polymer terahertz (THz) fibers were proposed in this paper, which were formed with honeycomb cladding and some elliptical air holes in the fiber core. The losses and mode birefringence for two different fibers are investigated by finite-different time-domain method. The results show that fiber 2 can achieve both high birefringence (larger than 0.022) and low confinement loss (0.01 dB/m) in a wide THz frequency range. Moreover, compared with a round solid-core fiber, guiding loss of the THz fiber caused by polymer material absorption can be reduced effectively as a part of the mode power is trapped in the air holes.