Abstract: Compared with the traditional fixed-wing-aircraft-borne synthetic aperture radar （SAR）， multi-rotor UAV SAR is more convenient to carry and operate. However， it is also more susceptible to air disturbance and its motion error has more serious spatial variability， which puts forward high requirements for motion compensation. In this paper， the signal model of frequency-modulated-continuous-wave （FMCW） SAR with line-of-sight （LOS） motion error was established， and the two-step motion compensation method of FMCW SAR was derived， then the shortcomings of this algorithm and its improved algorithm in the application of multi-rotor UAV SAR were pointed out. In order to make the compensation of SAR based on the inertial measurement unit （IMU） data more accurate， this paper proposed a "range-cell-by-cell compensation method". The method calculates the corresponding compensation function for each range cell， and only outputs the data of the corresponding range cell after each compensation. Compared with other compensation methods， this method can compensate the space-variant slant range error and velocity error more accurately and reduce the influence of residual error on each imaging step. Finally， the effectiveness of the algorithm was verified by simulation.