This paper analyzes an S-band relativistic multiple-beam klystron amplifier with three-dimension electromagnetic codes, including the high frequency characteristics analysis and beam-wave interaction studies. The simulation results show that the adoption of coaxial resonant cavity can reduce the adverse effect of electric field asymmetryin the cavity, for the beams do not have to concentrate at the center to pass through the cavity, the use of multiple-beam can reduce the magnetic field strength for beam transport to about 0.4 T. Witha 700 kV, 5.8 kA electron beam under 0.4 T magnetic field, the amplifier with three coaxial resonant cavities has a peak pulsed output power of 1.4 GW with a corresponding electronic efficiency of 35%.