The advantages of the tri-axial relativistic klystron amplifier and the multi-beam klystron amplifier are analyzed, and then an X-band coaxial multi-beam relativistic klystron amplifier is designed in order to increase the output microwave power and frequency. Based on the results from partial-in-cell simulation, the experiment is performed on the Sinus accelerator. In experiment, the transmission and bunching of electron beam are analyzed, and then the amplifier is driven by a beam of 5.3 kA at 670 kV, and the maximum output power is 420 MW when input power is 30 kW, and frequency is 9.375 GHz. The experiment proves that a ten kW-level input power can drive the X-band coaxial multi-beam relativistic klystron amplifier to generate more than one hundred MW-level output power.