Abstract: In order to provide a theoretical basis for the construction of a coaxial Bragg resonator with high-order single-mode operation at THz frequency. Based on the mode coupling theory, the influence of different ripple depths, different ripple taper shapes and different taper angles on the bandwidth and center frequency offset characteristics of the working mode and the competitive mode in the high-frequency high-order coupling mode of terahertz frequency are compared and studied. The results show that the bandwidth of the working mode and the competition mode becomes wider with the deepening of the ripple depth, but the center resonant frequency point almost does not shift, and the band gap overlap will worsen with the deepening of the ripple depth, which is not conducive to the mode selection; with the increase of the taper angle, the central frequency of the operating mode does not shift under the positive taper ripples structure, and the center frequency of the competition mode is close to the center frequency of the operating mode, which is not conducive to the suppression of the band gap overlap; with the increase of the taper angle, the center frequency of the competition mode of the negative taper ripples is far away from the operating mode, which is a good suppression of the band gap overlap; the positive taper ripples structure and negative taper ripples structure have little effect on the bandwidth. These characteristics are beneficial to expand the performance of the coaxial Bragg structure as a reflector and filter.