The existence of strong background clutter often masks the desired target response, and thereby significantly affects the ground-penetrating radar (GPR) target detection. This effect is even more pronounced for rough terrain and shallow buried targets. Therefore, it is essential to eliminate the clutter to facilitate the target detection. In this article, a deep-learning-based attention U-Net model is proposed for clutter removal of GPR data. This technique integrates a channel attention module (CAM) and a spatial attention module (SAM) with a U-Net architecture to enhance the clutter removal performance. The proposed model implicitly learns to suppress irrelevant clutters while emphasizing the desired target. The effectiveness of the proposed clutter removal approach is validated on synthetic and measured data through visual inspection and quantitative evaluation.