Deep learning algorithms have been widely used in ship detection with synthetic aperture radar (SAR). However, the complex background, clutter noise, and large span of ship sizes have adverse effects on the feature extraction, which seriously limits the ship detection accuracy. To address this issue, a cross-scale regional prediction-aware network (CSRP-Net) is developed to advance the ship detection performance in SAR images. First, the cross-scale self-attention (CSSA) module is designed to suppress the influence of noise and complex backgrounds and enhance the ability to detect multiscale targets. Furthermore, a regional prediction-aware one-to-one (RPOTO) label assignment is proposed to select the foreground samples more conducive to classification and regression in the training stage. Extensive experiments have proved that the designed method can significantly improve the detection performance against several start-of-the-art algorithms on two classical benchmark datasets.