Spaceborne spotlight SAR mode has drawn attention due to its high-resolution capability, however, the studies about moving target detection with this mode are less. The paper proposes an image sequence-based method entitled modified logarithm background subtraction to detect ground moving targets with Gaofen-3 Single Look Complex (SLC) spotlight SAR images. The original logarithm background subtraction method is designed by our team for airborne SAR. It uses the subaperture image sequence to generate a background image, then detects moving targets by using image sequence to subtract background. When we apply the original algorithm to the spaceborne spotlight SAR data, a high false alarm problem occurs. To tackle the high false alarm problem due to the target’s low signal-to-noise-ratio (SNR) in spaceborne cases, several improvements are made. First, to preserve most of the moving target signatures, a low threshold CFAR (constant false alarm rate) detector is used to get the coarse detection. Second, because the moving target signatures have higher density than false detections in the coarse detection, a modified DBSCAN (density-based spatial-clustering-of-applications-with-noise) clustering method is then adopted to reduce false alarms. Third, the Kalman tracker is used to exclude the residual false detections, due to the real moving target signature having dynamic behavior. The proposed method is validated by real data, the shown results also prove the feasibility of the proposed method for both Gaofen-3 and other spaceborne systems.