A photonic bandgap fiber was designed based on the novel Terahertz lowloss material Topas cyclic olefin copolymer. Fiber cladding was formed by arranging hexagonal air holes with rounded corners in triangular lattice pattern in the background of Topas. A rhombic hollowcore with rounded corners was formed by omitting four central air holes of the cladding structure. Propagation properties in the terahertz band of the fiber were investigated by using the finite element method. Numerical results indicate the fiber has a photonic bandgap within a broadband area about 0.3 THz around 1.5 THz, and THz wave is welled confined in the air core. Birefringence of the order of 10－3 was obtained. Loss of the xand ypolarized fundamental modes is less than 0.1 cm－1 within 1.4~1.6 THz, and reaches the minimum value of 0.029 1 cm－1 and 0.028 7 cm－1 at 1.53 THz and 1.5 THz, respectively. Structure of designed terahertz Topas photonic bandgap fiber is simple, feasible for fabrication and bendable because of the relatively small diameter.