A new type of terahertz photonic crystal waveguide, whose clad made of silicon contains periodic circular air holes arranged as triangular lattice and core is polythene (PE), is presented. Bandgap distribution characteristic of this photonic crystal terahertz waveguide and how air-filling factors affect the bandgap distribution characteristic are investigated by plane wave method (PWM). Then loss characteristics of the photonic crystal terahertz waveguide with different parameters are computed by finite-difference frequency-domain method (FDFD). Results show that this waveguide is a sort of photonic band gap guiding fiber with good capability to transmit terahertz wave. With higher air-filling factors, larger spacing between air holes and more circular structures in the cladding layer, lower leakage loss could be achieved. The lowest loss could be less than 1.5 dB/km if parameters are chosen appropriately.