Synthetic aperture radar (SAR) is a powerful imaging technology. Due to the coherent imaging mechanism of decimeter waves, it can obtain ground reflection information regardless of cloud, fog, rain, snow, and light conditions. However, the detection of ship targets in SAR images remains challenging due to the complex scattering mechanisms and background interference. Hence, we propose a novel ship detector, called SAR-DETR, leveraging the DETR architecture enhanced with a feature pyramid network (FPN) to improve the extraction of both low-level and high-level features. Our approach addresses the limitations of traditional deep learning methods, such as high computational complexity and inadequate feature extraction capabilities in SAR imagery. Through extensive experiments on the SSDD dataset, our model demonstrates significant improvements in detection performance, achieving an accuracy of 90.64% and outperforming state-of-the-art methods like YOLOv5, Faster R-CNN, and RetinaNet. The results indicate that the proposed SAR-DETR effectively reduces missed detections and false positives, showcasing its potential for real-time maritime surveillance applications.