In the area of SAR imaging, it is of interest to be able to focus moving targets. In this paper, an algorithm for moving target focusing is presented. The algorithm is able to refocus a smeared moving target in a SAR image processed at one relative speed to the correct one.. The algorithm works in the frequency domain and is based on the Range Migration algorithm. The refocusing can be made on the whole SAR image or small sub images corresponding to physical areas of interest for the end user. By applying the algorithm to a small image, the computational cost is greatly reduced compared with using the full SAR image. The performance is illustrated by applying the algorithm to simulated SAR data according to the parameters for the LORA system.