The propagation properties of polarized Hermite-Cosh-Gaussian(HChG) beams along the optical axis of uniaxially anisotropic crystals are investigated.Based on the paraxial vectorial theories of beam propagation,an analytic expression of the diffraction light field is obtained.The effects of the anisotropy on the polarization properties of the diffracted HChG light beams have also been explained by means of the numerical method.The results elucidate that the distributions of the optical field change with the different parametric variation for the polarized beams in the anisotropic crystals.