Abstract: To meet the high power and high gain requirements in engineering applications, we've designed a three-dimensional whole tube model for an X-band high-power high-gain multi-beam relativistic klystron amplifier. This paper presents the high frequency characteristic analysis and the tube with the integrated model. The input cavity structure with bilateral symmetric coupling hole is designed to reduce the influence of the input waveguide on the field uniformity of the input cavity gap. A multi-cavity and multi-gap modulation structure is adopted to reduce the requirement of input microwave power and improve the amplification gain. Moreover, the multi-gap spreading interaction extraction structure is analyzed and designed to improve the power conversion efficiency and reduce the surface electric field intensity, so as to control the risk of RF breakdown of the device. A three-dimensional full electromagnetic particle in cell code is used to simulate the absorption of injected microwave, and the fundamental harmonic modulated current when electron beams propagate through the input cavity and middle cavity gaps have also been simulated. A 3.2 GW averaged microwave power over the oscillator period is generated by simulation with 900 kV electron beam voltage, 9 kA current and 1 T leading magnetic induction intensity, the efficiency is 40% and the amplification gain is 60 dB. In the experiment, a 0.99 GW average microwave power was generated with 550 kV electron beam voltage, 5.1 kA current, 35% efficiency and 53 dB amplification gain.