Abstract: Because of the special track of circular SAR, the imaging algorithms of SAR in linear track can not be used in processing the circular SAR data directly. However, the response functions of the circular SAR systems can remain the consistency by changing the same aspect angle both of the target and the starting position of the radar. Because of this characteristic, circular SAR can be processed in the azimuth frequency domain by using the fast imaging algorithm of SAR in linear track for reference. In this paper, the exact signal spectrum expressions of circular SAR are derived. By using the reasonable approximations of the exact signal spectrum expressions, the fast imaging algorithms are presented. The simulations show the good performance of the proposed algorithms.