In this study, an iterative minimum entropy algorithm is proposed for synthetic aperture radar (SAR) refocusing on moving targets with data of the defocused region of interest (ROI). The image entropy of the ROI data is modelled as a function of the phase compensation parameter. Then, an image entropy surrogate function is constructed to iteratively estimate the phase compensation parameter. With the convergence of iterative estimation of the phase compensation parameter, a refocused image of the moving target can be achieved. By directly operating on the small-size defocused ROI data, the computational burden is significantly reduced and most of the clutter is suppressed. Different from the existing ROI-based methods for SAR refocusing of moving targets, the proposed algorithm does not need any prior parameters. The performance of the proposed algorithm is demonstrated by using simulated data and real SAR data. Compared with some existing methods, the proposed method can produce slightly better-refocusing effect with less computational complexity.