The accurate calibration of the beam energy of the circular electron-positron collider (CEPC) is performed to accurately measure the mass width of Higgs particle and the mass of W/Z boson, thus providing the basic experimental basis for the accurate test of the standard model. Based on this, the error control of beam energy is required to be at a level of 10 ^–5. Compton backscattering method is suitable for high precision calibration of beam energy in the Hundred GeV high energy electron collider. In this work, the CEPC beam energy is predicted to reach a theoretical accuracy of about 3 MeV by using the accurate measurement of the scattered photon energy after microwave electron Compton backscattering. Firstly, TM ₀₁mode microwave transmission in circular waveguide is selected according to the design requirements, and the electromagnetic field distribution and Poynting vector under this condition are solved. According to the photon distribution and transmission in the waveguide, the design idea is proposed to simplify the complexity of calculation, and the parameters conforming to the design requirements are solved by combining the simultaneous equations of the high purity germanium detector sensitivity and the background of synchrotron radiation. Using the optimal set of waveguide inner diameter, microwave wavelength and electron incident angle data, the derivative of the differential scattering cross section with respect to energy and the collision brightness are obtained when the microwave power is 100 W. The scattered photon density of 15 MeV energy is further obtained, and the signal-to-noise ratio is analyzed according to the photon density of synchrotron radiation under this energy. The feasibility of the scheme is demonstrated theoretically and the technical difficulties and problems to be further studied are discussed.