We report a numerical investigation on terahertz wave propagation in plastic photonic band-gap fibres which are characterized by a 19-unit-cell air core and hexagonal air holes with rounded coers in cladding. Using the finite element method, the leakage loss and absorption loss are calculated and the transmission properties are analysed.The lowest loss of 0.268 dB/m is obtained. Numerical results show that the fibres could liberate the constraints of background materials beyond the transparency region in terahertz wave band, and efficiently minimize the effect of absorption by background materials, which present great advantage of plastic photonic band-gap fibres in long distance terahertz delivery.