The design of a W-band four-cavity gyroklystron amplifier is presented. The device operates in the fundamental harmonic TE01 circular electric mode. The 70 kV, 6 A beam is produced by a double anode magnetron injection gun (MIG) with an average perpendicular-to-parallel velocity ratio of 1.5 and a parallel velocity spread of less than 4%. Particle-in-cell (PIC) simulations have been performed to predict general RF performance for various parameters. The simulated results show that the designed gyroklystron amplifier can produce about 35 dB gain, 800 MHz bandwidth and 100 kW peak output power with power conversion efficiency of 23.8% for a beam with 4% axial velocity spread.