The space charge limiting current in cylinder drifting tube and coaxial drifting tube and the energy that could be obtained and also the restrict magnetic field are analyzed, and the results show that it is propitious to change the energy of electron beam into microwave power in the coaxial conduit. The advantages of the tri-axial relativistic klystron amplifier and the multi-beam klystron amplifier are analyzed, then an x-band coaxial multi-beam relativistic klystron amplifier is designed by using a three-dimensional particle simulation software, and the transmition and the bunching of electron beam are analyzed. A 1.23 GW averaged microwave power over the oscillator period is generated by simulation with 600 kV electron beam voltage, 5 kA current and 0.8 T leading magnetic field density, the frequency is 9.37 GHz and the efficiency is 41%.