A high-birefringence and low-loss terahertz (THz) hollow-core anti-resonant fiber (THz HC-ARF) is designed and analyzed numerically by the finite element method (FEM). The THz HC-ARF is composed of an elliptical tube as the core for high birefringence guidance and a pair of symmetrical slabs arranged vertically as the cladding to attain low loss. Numerical analysis indicates that the birefringence reaches 10-2 in the transmission window between 0.21 and 0.35 THz. The highest birefringence is 4.61 × 10-2 at 0.21 THz with a loss of 0.15 cm-1. To verify the theoretical results, the THz HC-ARF is produced by three-dimensional (3D) printing, and the transmission characteristics are determined by THz time-domain spectroscopy (THz-TDS). High birefringence in the range of 2.17 × 10-2 to 3.72 × 10-2 and low loss in the range of 0.12 to 0.18 cm-1 are demonstrated experimentally in the 0.2 to 0.27 THz transmission window. The highest birefringence is 3.72 × 10-2 at 0.22 THz and the corresponding loss is 0.18 cm-1. The THz HC-ARF shows the highest birefringence besides relatively low loss compared to similar THz HC-ARFs reported recently.