Using a self-consistent nonlinear code and particle-in-cell simulation, the beam-wave interaction of a W-band four-cavity gyroklystron amplifier has been analyzed. The gyroklystron amplifier operates in the fundamental harmonic TE 01 circular electric mode. The dependence of the efficiency and gain on the input power and the electron velocity ratio are studied. The effect of the electron velocity spread on the bandwidth and the electronic efficiency is analyzed. The simulated results show that the designed stable gyroklystron amplifier can produce an output power of over 142 kW, 33.8% electronic efficiency, 37 dB gain, and a 3 dB bandwidth of 1 GHz for a 70 kV, 6 A electron beam.