Abstract: Earth-based radar mapping of the moon can obtain the electromagnetic scattering characteristics and topographic features of the lunar surface, which can be used for scientific research on the moon. Earth-based radar mapping technology of the moon is the application of synthetic aperture technology to astronomical detection. Delay Doppler technology is the most widely used technology for earth-based radar astronomical mapping, and its key lies in motion compensation. At present, foreign research in the field of earth-based astronomical radar has become mature, while my country is in its infancy. In order to solve the difficult problems in earth-based radar mapping of the moon, this paper firstly analyzes the key problems of delay Doppler mapping theory based on the geometric model of the earth-moon motion, including the mapping principle, resolution and blur problem. Next, this paper proposes a parametric motion compensation algorithm, which uses image entropy as an evaluation index to search for parameters, and uses cuckoo search algorithm to improve the efficiency of parameter search. Finally, the effectiveness of the algorithm is verified by simulation, which provides technical support for future experiments.