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We have proposed a novel kind of photonic crystal fiber which contains two asymmetric cores. The birefringence and the dispersion are numerically analyzed based on finite element method when the size of the air holes and the pitch of two adjacent air holes are changed. It is shown that the proposed photonic crystal fiber has high birefringence up to the order of 10−2 and double-zero dispersion points are at the wavelengths of 1310 nm and 800 nm, simultaneously. At the same time, the normalized power and the extinction ratios of the proposed photonic crystal fiber have been simulated. It is demonstrated that, at the wavelength of 1310 nm, the x-polarized mode and the y-polarized mode are separated when the propagation distance is 2.481 mm.