Based on the difference in working mode between Frequency Modulated Continuous Wave (FMCW) Synthetic Aperture Radar (SAR) and Pulse Synthetic Aperture Radar, which leads to a different form of the echo, this paper establishes the model of the Spotlight FMCW SAR receiving signal, analyzes its characteristics, and reveals the effect of Doppler frequency shift induced by the continuous motion in range direction while radar is transmitting and receiving signals, which affects azimuth focusing ultimately. For the problem of azimuth spectral folding, this paper adopts azimuth pre-filtering processing, which increases the sampling frequency through interpolation. Since azimuth pre-filtering can realize bulk azimuth data compression, the number of azimuth points does not increase significantly. Finally, based on the Frequency Scaling Algorithm, residual data focusing can be achieved. Point targets simulation verifies the analysis and validity of the algorithm. In addition, for the Doppler frequency shift induced by the continuous motion while radar is transmitting and receiving signals, we also analyze its effect on imaging and give the corresponding compensation method.