Video synthetic aperture radar (SAR) has been found to be very valuable for detecting and tracking moving targets and observing areas of interest. Shadows produced by target motion in sequential radar images can be used to detect targets themselves. Since existing deep learning shadow detection methods often require many hand-designed components, in this paper, we propose a shadow detection method for video SAR moving target based on transformer, which is named Deformable Shadow-DETR. Deformable Shadow-DETR can better extract shadow features, and use the transformer encoder-decoder network to treat shadow detection as a direct set prediction problem, eliminating the need for cumbersome hand-designed components. Experiments on the real video SAR data published by the Sandia National Laboratories show that our proposed moving target shadow detection method can achieve excellent performance.