In synthetic aperture radar (SAR) images, moving targets are usually smeared and/or imaged at incorrect positions due to the target motions during the SAR integration time. Moreover, since a high-resolution wide-swath SAR system is operated with a rather low pulse repetition frequency, a moving target will cause multiple ghost targets in the reconstructed SAR image. A new space-time adaptive processing framework is proposed in this paper for removing moving target artifacts in SAR images. In this new framework, the dynamic steering vector concept is proposed. In addition, this paper develops a moving target processing scheme for clutter suppression and moving target imaging and location for a high-resolution wide-swath SAR system. Finally, we locate the well-focused moving targets at the stationary scene image without any disturbing artifacts. The simulated and real data are used to validate the effectiveness of our proposed method.