A novel circuit with broad bandwidth is designed for the W-band Extended Interaction Klystron (EIK) in this paper. The three operating modes ($\pi$ mode, $\pi+1$ mode, $\pi+2$ mode) with a certain frequency interval among them are analyzed, which results in expanding bandwidth of the circuit. The circuit is powered under condition of a 2A, 2. 7kV pencil beam with 0.2mm radius and 11mm EIK circuit length, whose simulation results predict that the saturated output power is 91 0W and 3dB bandwidth is greater than 750 MHz.