Based on a full-vector model, a theoretical study on a kind of high birefringence photonic crystal fibre is presented.Due to introducing air holes of two different sizes into the cladding, twofold rotational symmetry was obtained. We demonstrate the possibility of achieving high birefringence that is at least one order of magnitude higher than that of conventional polarization-maintaining fibres. The dependences of modal birefringence, modal field and differential group delay on the structure parameter of the fibres are discussed in detail. The numerical results are in very good agreement with the experimental results in the literature.