Abstract: With 3D full electromagnetic code, an S-band overlapped mode two-gap output cavity for broadband relativistic klystron amplifier has been designed and calculated, and there is two modes in the two-gap output cavity. It is found that the two modes will be overlapped partially by adjusting the structure of output caviy and it is beneficial to expand the bandwidth of output structure. A 2.0GW averaged power over the oscillator period is generated by simulation, with 850kV electron beam voltage, 7.6kA current and 90% depth of the modulated current using the two-gap output cavity. The centric frequency is 2.85GHz. The 3dB bandwidth is about 10%.