An extended interaction klystron (EIK), which is composed of an input cavity and an output cavity both based on 8 periods of staggered double rectangular waveguide structure (SDRWS) and an intermediate cavity based on 6 periods of SDRWS, is calculated in detail on computer. After calculating reflection coefficient S11of the input cavity and output cavity and the eigenmodes of the intermediate cavity, the structural parameters of the input cavity and output cavity and the intermediate cavity are determined, then PIC simulation is done to predict the EIK’s performance, the results show that the EIK has an 1 GHz 3 dB bandwidth (219.5-220.5 GHz), a 456 W maximum power and a 40.06 dB maximum gain. Furthermore, stagger tuning by adjusting the structural parameter a of the intermediate cavity is performed to analyse how a affects the EIK’s performances, and the results show that the 3 dB band of the EIK mainly depends on the passband of the input cavity and output cavity, it also depends on the resonant frequency of the intermediate cavity in some cases. When the resonant frequency of the intermediate cavity is located at the lower or higher ends of the passband of the input cavity and output cavity, the 3 dB band of the EIK may be extended to certain extent. Particularly, when the resonant frequency of the intermediate cavity is located at or beyond the higher ends of the passband of the input cavity and output cavity, it is verified that the EIK has steady output signal featuring with pure spectrum and flat gains over the 3 dB band. The final results of the stagger tuning show that , when the structural parameter a of the intermediate cavity is 0.747 mm, the EIK reaches almost the optimum performances, with an 1.2 GHz 3 dB bandwidth (219.5-220.7 GHz), a 630 W maximum power companied with a 11.3% efficiency, and a 47 dB maximum gain.