To solve the problem that W-band klystron is difficult to achieve CW (continuous wave) high power, we propose a W-band CW sheet beam extended-interaction klystron (EIK) high frequency circuit operating at TM₃₁-2π mode. A sheet electron beam with a voltage of 20 kV, a current of 0.65 A and the dimension of 2.5 mm×0.3 mm is used. The high frequency system adopts five dumbbell type five-gap cavities and the output system adopts symmetrical output waveguide. By optimizing high-frequency structural parameters, the simulation results of 3D PIC show that more than 1200 W power can be obtained at an input power of 0.2 W, and the electron efficiency and gain are 9.35% and 37.8 dB respectively. In terms of sensitivity and error stability of high-frequency parameters, TM₃₁ mode and TM₁₁ mode are compared and analyzed in detail.