A 3 mm band four cavity gyroklystron was designed and simulated. The working mode was the low loss TE01 mode. Linear theory was applied to determine the initial operating parameters. The famous FEM code HFSS was used to optimization design of every single cavity. PIC simulation code was used to design the interaction circuit. Studies to determine the optimal stagger tuning and cavity Q values were performed. Circuit stability was investigated and the effect of beam parameter variation on circuit performance was also studied. Simulations show that a four cavity circuit operating in the TE01 mode at the fundamental of the cyclotron frequency can achieve 139 kW peak output power, 35.6% efficiency and 28.4 dB gain at a center frequency of 93.7 GHz with about 600 MHz full width half maximum (FWHM) bandwidth for a 65 kV, 6 A, pitch angle α(V⊥/V∥)1.5 and velocity spread 0% beam.