Synthetic Aperture Radar (SAR) can acquire high-resolution radar images with the pulse compression and coherent accumulation techniques. However, it usually suffers from various kinds of active jamming in practical applications. The quality of imaging results is therefore degraded. To deal with this problem, some jamming suppression methods were presented in the preceding works. However, these methods rely on the handcrafted features. They are specific to certain jamming mode, or certain dataset. They are not effective in the realistic scenarios. To solve these problems, a novel SAR jamming suppression method is proposed in this paper. Different from the preceding works, a new Transformer-based U-shaped architecture is first developed. It is then used to learn the high-level representations from the input degraded image. The learned features are then used to predict the clean images. The loss function is then used to measure the difference between the predicted results and the truth images. The parameters of deep architecture can be therefore updated. Compared with the preceding works, the proposed method is effective for all of the jamming modes used for training. Likewise, the imaging quality can be improved much better than the classical strategies. Multiple rounds of experiments are performed. The results demonstrate the advantages of the proposed method in comparison to the state-of-the-art.