The concept of lunar-based earth observation concept has been proposed in order to improve the large scale observation ability towards global changes.Because the signal to noise ratio of lunar-based monostatic synthetic aperture radar (SAR) decreases seriously due to the two-way propagation,a novel lunar-earth bistatic SAR operating mode was studied.Considering the complex relative movement among lunar,earth and satellite brings difficulty to SAR imaging,a rectangular plane echo model was built according to the geometrical relationship of lunar,earth and satellite.Due to the curves of lunar and satellite orbits,the modeling error was analyzed,and a precise two-dimensional frequency domain expression of echo was also deduced.Then a fast back projection based SAR imaging algorithm was designed to compensate the azimuth variant modeling error.The calculation speed was increased by frequency domain sub-aperture imaging and spectrum combination.The signal noise ratio of lunar-earth bistatic SAR is inversely proportional to the distance between earth and lunar through analysis,simulated X-band SAR data sets are used to validate the effectiveness of the proposal to deal with lunar-earth bistatic SAR imaging.