The development of the vector polarized beam presents a new requirement for the mode calculation of the polarization-sensitive resonator. Derived from Fox-Li iterative method and Jones vector theory, a vector Fox-Li iterative method for polarization-sensitive resonator is presented, which can calculates the vector polarization mode in the polarization-sensitive resonator, including the azimuthally polarized TE01* mode and the radially polarized TM01* mode. The vector polarization modes of a spherical polarization-sensitive resonator are obtained by Matlab numerical calculation with this method. The result is coincident with the theory. Then, the 2.17 kW azimuthally polarized beam is obtained based on a fast axial flow (FAF) CO2 laser platform using the combined axicon as the rear mirror of the resonator. And it is consistent with the simulated results with vector Fox-Li iterative method, which experimentally corroborates the validity and accuracy of the vector Fox-Li iterative method. The vector Fox-Li iterative method is of great significance for the analysis and design of polarization-sensitive resonator.