We report the results of our investigation on the loss property of a birefringent photonic crystal fibre (PCF) basedon a particular periodic arrangement of air-holes and pure silica. The structure of the birefringent PCF, whoseair-hole diameter in one ring is always larger than the next inner ring, presents an obviously low confinement lossthan the one whose air-hole (except those on the horizontal line) diameter is constant. It is shown from numericalresults that a four-ring PCF with birefringence B = 5 × 10-4 and fast axis confinement loss of 4.5 × 10-3 dB/kmat wavelength of 1.55μm can be designed.