The anamorphic optical system is a relatively special optical system with bi-planar symmetry, whose structure gives rise to non-rotationally symmetric polarization aberrations. Aiming at the problem, we construct a catadioptric anamorphic optical system. Furthermore, we also systematically analyzes the polarization aberration of this system and its effect on the point spread function. Simulations of a catadioptric anamorphic optical system based on a three-dimensional polarized light trace are performed to obtain detailed data on the polarization aberration and to compute the diattenuation and retardance distribution characteristics of individual surfaces, as well as the Jones pupil, the amplitude response matrix, the point spread function, and the polarization crosstalk contrast of the system. The maximum diattenuation is 0.145, and the maximum retardance is 1.46×10^-2 rad, both occurring at the secondary mirror position. The amplitude response function of the optical system with a 2∶1 anamorphic ratio has a 40.6% difference between the polarization crosstalk term in the long and short focal end directions, and the anamorphic optical systems contrast is limited by an order of magnitude of 10^-6 by polarization crosstalk. Polarization aberration in high-precision anamorphic optical systems is not negligible. The effects of polarization aberration can be reduced by film layer design and catadioptric structure. The conclusions of this study can serve as a reference for designing anamorphic optical systems in deep space exploration and coherent communication systems.