Based on the full-vector finite element method, the birefringence in microstructure fiber with squeezed hexagonal lattice is numerically analyzed. The correlation between the birefringence and the structural parameters, incidence wavelength is obtained. The numerical results show that the birefringence is sensitive to wavelength, and can be achieved by a magnitude of 10-3 with a proper design and the fast and slow axes can swap as incidence wavelength is changed. To simulate the practical situation, each air hole diameter is assumed with a Gaussian distribution. The birefringence is found to be largely dependent on the variation of air hole diameter. In the statistical analyses, the correlation between the variation of air hole diameters and the birefringence in such microstructure fiber is obtained. One important result is that the non-intentional birefringence depends on the mean air hole diameter, and a increase of the size of the fiber structure the birefringence.