Abstract: Cyclotron auto-resonance accelerator (CARA) has very high acceleration efficiency, and has a very good application prospect in the field of low energy and high power electron beam. Since the accelerating cavity of a CARA is immersed in the solenoid magnetic fields, the electron beam spirals forward under the constraint of the axial static magnetic field and keeps synchronization with the TE₁₁ mode microwave field in the accelerating cavity and is continuously accelerated transversely. The output energy of electron beam does not increase with acceleration monotonously but is determined by the reciprocal parameters, such as the electron beam injection energy, axial static magnetic field, accelerating cavity waveguide length and the amplitude of microwave electromagnetic field. In this paper, the effects of these reciprocal parameters on the output energy of the electron beam were analyzed theoretically. Numerical calculations based on the electromagnetic simulation code CST and the particle tracking code were done to study the constraint relationship of the reciprocal parameters. The designed output energy is achieved after optimization of the reciprocal parameters.