An optical resonator with a 90° cone reflector has a better misalignment tolerance because of its special structure. In this paper, a high-power transverse flow CO2 laser is selected as a model for numerical simulation, and the Fox-Li iterative approach has been used to analyze the output beam mode of the laser resonator. Calculation process is simplified when the beam transformation occur at 90° cone reflector. Because a 90° cone reflector is a no-paraxial device, and linear polarization is not preserved by the reflection. A modified vector method is used to analyze mode distribution of the output beam, and the results show that when the reflectivity difference between P and S polarizations is more than 3%, the radially polarized or azimuthally polarized beam with a polarization purity of 1 can be obtained by such resonator.