This work focuses on multi-target tracking in Video synthetic aperture radar. Specifically, we refer to tracking based on targets' shadows. Current methods have limited accuracy as they fail to consider shadows' characteristics and surroundings fully. Shades are low-scattering and varied, resulting in missed tracking. Surroundings can cause interferences, resulting in false tracking. To solve these, we propose a shadow-oriented multi-target tracking method (SOTrack). To avoid false tracking, a pre-processing module is proposed to enhance shadows from surroundings, thus reducing their interferences. To avoid missed tracking, a detection method based on deep learning is designed to thoroughly learn shadows' features, thus increasing the accurate estimation. And further, a recall module is designed to recall missed shadows. We conduct experiments on measured data. Results demonstrate that, compared with other methods, SOTrack achieves much higher performance in tracking accuracy-18.4%. And ablation study confirms the effectiveness of the proposed modules.