A new strong coupling multi-gap output structure has been developed as the output cavity of Ka band sheet beam klystrons. This structure has a better output coupling characteristics and better shape of electric field. Moreover, when the drift tube of the output cavity is cut-off in the operating frequency, an ideal field shape can be obtained as to support more efficient beam-wave interaction. An analysis of the distribution of the surface current supports the design theoretically. A stable output power curve can be observed at the center frequency by using particle-in-cell simulations, where the interaction efficiency is more than 50% and the 3dB bandwidth is about 75MHz.