In a typical triangular arrangement of photonic crystal fiber (PCF), each air-hole is replaced by a pair of twin air-holes. Two neighboring air holes with the same spacing and fixed axes direction come into being twin air holes pairs and it is the basic cell in the cladding of PCF.In the central of section, not missing one air hole but missing a pair of twin air holes with higher refractive index material can localize optical field and become the core of PCF. All twin air holes are regularly arranged according to triangular arrangement in the cladding. In this novel PCF, an asymmetry character is aroused because of all twin air holes with identical axis direction, and birefringence relevant to axes direction of twin air holes is formed. Finite difference (FD) method is used to analyze modal character of PCF. The results of numerical calculation indicate that, the effective refractive index difference between two orthogonal directions Δneff can reach the magnitude of 10-4. Especially, the structure parameter of twin air holes can change birefringence in slight, such as increasing air hole size or reducing spacing of two air holes within every twin air holes all can increase birefringence effect.