Abstract: The planer logarithm spiral slow wave circuit can effectively reduce the phase velocity of radial electromagnetic wave. For such slow phase velocity, the accelerating voltage can be as low as hundreds volts. Using electromagnetic simulation software HFSS, simulation of dispersion, synchronization, attenuation, transition characteristics of the planner logarithm spiral slow wave circuit and its relationship with the structure at 20~40GHz were carried out. By choosing appropriate slow wave structure, the dispersion curve is gently smooth. Attenuation is relatively small, the electron beam and the electromagnetic wave interact effectively. have a well propagation character.