Based on the paraxial vectorial theory of the propagation of beam in uniaxially anisotropic medium,the analytical formula for an elliptical Gaussian beam propagating in uniaxial crystal orthogonal to the optical axis is derived. And some numerical simulations were preformed to study the effect of the anisotropy on the polarization property of the diffracted elliptical Gaussian beam in the output plane. The results show that the linear polarization state and the symmetry of beam cannot remain unchanged during propagation due to the anisotropy of crystals.