The propagation of sinh-squared-Gaussian beams is investigated and the analytic solutions are obtained by means of an angular spectrum technique in uniaxially anisotropic crystals orthogonal to the optical axis. The propagation properties of the polarization components in crystals originating from sinh-squared-Gaussian beams are discussed with numerical method. The results show that the polarization properties cannot remain the same during propagation due to effects of anisotropic crystals. The field distribution of the beam polarized along the x-direction derives a y component. Along with the increase of the transmission distance, the polarization amplitude of the extraordinary ray along the x axis and the z axis are reduced, and the intensity also decreases. In addition, the propagation of the sinh-squared-Gaussian beams in anisotropic uniaxial crystals orthogonal to the optical axis can be influenced by the parameter β, and different β brings about different intensity distribution.