Output cavity has great impact on the efficiency and peak power of high-power klystron. To increase the peak power and improve efficiency, the double-gap coaxial output cavity in the X-band high-power multi-beam klystron is studied. An applicable structure can be achieved with parameter optimization, based on the theoretical calculation. With comparison of one-gap output cavity,it is confirmed that double-gap coaxial output cavity can increase the R/Q,decrease electric field of cavity gap,and extend bandwidth.