Abstract: The output circuit of high-order TM310 mode in single- and double-gap cylindrical coaxial cavities of klystron is designed. The gap impedances at the drift tube centers and corresponding output bandwidths are calculated, simulated and compared according to the equivalent circuit theory when the cavities are loaded with TE10 mode in empty rectangular waveguide. It is found that, double gap cavities have larger gap impedances and bandwidths than those of single gap cavities. By means of setting copper short circuit line in the inner side of output holes, the external quality factor is reduced and the mode uniformity in cavities is increased. This output circuit is suitable for high frequency, high power and narrowband klystrons. The research results are significant to output circuit design of high-order TM mode coaxial cavities of klystrons.