Abstract: The design of double-gap output cavity for relativistic klystron amplifier is provided. The angle and position of support rods and gap length are described. Using a three-dimension fully electromagnetic Particle-in-Cell (PIC) code, the simulation of microwave extraction from modulated intense relativistic electron beams which pass through double-gap output cavity is investigated, and the beams and double-gap output cavity geometry parameters are optimized. An output microwave power of 1.1 GW is generated by simulation, with an electron beam voltage of 640 kV, a current of 6 kA and 80% modulation depth of the fundamental wave. The efficiency is 28%. The S-band RKA double-gap output cavity was designed according to high frequency analysis and particle simulation results. Subsequently, the ex