Synthetic aperture radar (SAR) ship detection based on deep learning has been widely applied in recent years. However, two main obstacles are hindering SAR ship detection. First, the identification of ships in a port is seriously disrupted by the presence of onshore buildings. It is difficult for the existing detection algorithms to effectively distinguish the targets from such a complex background. Additionally, it appears more complicated to accurately locate densely arranged ships. Second, the ships in SAR images exist at a variety of scales due to multiresolution imaging modes and the variety of ship shapes; these pose a much greater challenge to ship detection. To solve the above problems, this paper proposes an object detection network combined with an attention mechanism to accurately locate targets in complex scenarios. To address the diverse scales of ship targets, we construct a loss function that incorporates the generalized intersection over union (GIoU) loss to reduce the scale sensitivity of the network. For the final processing of the results, soft nonmaximum suppression (Soft-NMS) is also introduced into the model to reduce the number of missed detections for ship targets in the presence of severe overlap. The experimental results reveal that the proposed model exhibits excellent performance on the extended SAR ship detection dataset (SSDD) while achieving real-time detection.