The random offset of hole-position or random variation of hole-diameter always occur during the actual manufacture process of asymmetric structure photonic crystal fibers. Birefringence of asymmetric photonic crystal fibers with circular air holes and photonic crystal fibers with elliptical air holes are studied numerically based on the finite element method under the perturbation circumstance. The results indicate that when the intrinsic-birefringence of asymmetric photonic crystal fiber is smaller, the random offset of hole-position has larger influence than the variation of hole-diameter. Birefringence resulted from perturbation is less sensitive to asymmetric structures with large pitch or small air-hole. Moreover, the desired birefringence can be obtained by controlling the relative size of the two air holes or the ellipticity of the elliptical-hole.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.