Sheet beam extended interaction klystron, which has both the advantages of sheet beam klystron and extended-interaction klystron (EIK), has become a key technique for developing high power microwave and millimeter-wave vacuum electron devices. An equivalent circuit of the five-gap output cavity for sheet beam EIK is proposed in this paper. The mode, resonant frequency, and the cavity impedance can be calculated by using the method of equivalent circuit efficiently. The bandwidth could be estimated by the curve of cavity impedance versus frequency. The influences of coupling coefficient (k) and external Q (Qe) on mode frequency interval and bandwidth are discussed. In order to test and verify the method of equivalent circuit, the 3D-PIC simulation of output cavity is conducted. The bandwidths under different values of external Q are calculated in two ways. The results accord well with each other. It is confirmed that the method of equivalent circuit for sheet beam EIK is accurate and credible. This is useful for the design of the whole tube.