In this paper, a multigap extended output cavity was designed by 3-D simulations, which served as the output cavity for a W-band sheet-beam extended interaction klystron (SBEIK). In our numerical design, the circuit dimensions were systematically optimized by parametric finite-difference time-domain simulations, and the equivalent circuit for the output cavity was also analyzed. The proper external loading was selected by using a region of loss in 3-D, and the output power was optimized. The results were verified by using the coupler and the waveguide. The 2π mode of the optimized five-gap extended output cavities had an ohmic Q (Q 0 ) of 1343.5, an external Q (Q e ) of 501.6, and a loaded Q (Q L ) of 365.2 at 94.5 GHz. The 3-D particle-in-cell simulations predict that the output cavity of the SBEIK (75 kV and 4 A) can stably produce more than 50 kW of output power using a prebunched beam.