With the increase in frequency, the output gain and bandwidth of microwave vacuum devices are subject to considerable limitations, which may be solved by extended interaction klystron. With the same working principle as high-power klystron’s, the extended interaction klystron uses distribution function cavity technology to expand its operating bandwidth and gain. In this paper, a Ku-band extended interaction klystron tube is designed and simulated with PIC (particle-in-cell) three-dimensional software and CST. At the working voltage of 30 kV, beam current of 8.5 A, when the PPM-Focusing system of 0.48 T is adopted, and the input power is 5.1 W, the microwave output can be obtained with an efficiency of 23%, peak power of 58 kW, 3 dB bandwidth of 306 MHz, and the largest in-band gain of 39