Abstract: Synthetic Aperture Radar using Frequency modulated continuous waveforms (FMCW SAR) has the advantages of low cost and low power consumption, which facilitates the development of small or micro SAR systems. The existing FMCW SAR imaging algorithms rely on wideband transmitted waveforms to achieve high range resolution. In this paper, we presented a new imaging algorithm for FMCW SAR. Besides the range resolution, this algorithm can exploit the good Doppler resolution provided by CWs by using the temporal/intrapulse Doppler in the imaging, which lead to a range resolution not dependent only on the bandwidth of the transmitted waveform and can provide good range resolution for narrowband cases. The performance of the presented algorithm was analyzed from the perspectives of algorithm flowchart, imaging look-direction and image resolution. Simulations verified the presented algorithm and the theoretical findings.