The energy measurement uncertainty of circular electron positron collider (CEPC) beam must be less than 10MeV to accurately measure the mass of the Higgs/W/Z boson. A new microwavebeam Compton backscattering method is proposed to measure the beam energy by detecting the maximum energy of scattered photons. The uncertainty of the beam energy measurement is 6MeV. The detection accuracy of the maximum energy of scattered photons need to reach 10 −4 . The high-precision gamma detectors can only be a high-purity germanium (HPGe) detector. It is a semiconductor detector, the effective detection range of the gamma energy is 100keV-10MeV. The maximum energy of the scattered photons is chosen to be the higher the better to reduce the influence of the synchrotron radiation background. Therefore, the maximum energy of the scattered photons is selected to be 9MeV. Therefore, the initial photons should be microwave photons to collide with the electrons with the energy of 120GeV on CEPC. The cylindrical resonant cavity with T M010 mode is selected to transmit microwaves. After Compton backscattering, the scattered photons emit from the vacuum tube of the synchrotron radiation and the energy is detected by the HPGe detector. The structure of shielding materials with polyethylene and lead is designed to minimize the background noise, such as the synchrotron radiation and the classical radiation from the electron beam in the cavity. The hole radius in the side wall of the cavity is about 1.5mm to allow the electron beam to pass through. The computer simulation technology (CST) software shows that the influence of the hole radius on the cavity field is negligible, and the influence of the hole radius on the resonance frequency can be corrected easily.