Synthetic aperture radar (SAR) is an active microwave imaging sensor with the capability of working in all-weather, all-day to provide high-resolution SAR images. Recently, SAR images have been widely used in civilian and military fields, such as ship detection. The scales of different ships vary in SAR images, especially for small-scale ships, which only occupy few pixels and have lower contrast. Compared with large-scale ships, the current ship detection methods are insensitive to small-scale ships. Therefore, the ship detection methods are facing difficulties with multi-scale ship detection in SAR images. A novel multi-scale ship detection method based on a dense attention pyramid network (DAPN) in SAR images is proposed in this paper. The DAPN adopts a pyramid structure, which densely connects convolutional block attention module (CBAM) to each concatenated feature map from top to bottom of the pyramid network. In this way, abundant features containing resolution and semantic information are extracted for multi-scale ship detection while refining concatenated feature maps to highlight salient features for specific scales by CBAM. Then, the salient features are integrated with global unblurred features to improve accuracy effectively in SAR images. Finally, the fused feature maps are fed to the detection network to obtain the final detection results. Experiments on the data set of SAR ship detection data set (SSDD) including multi-scale ships in various SAR images show that the proposed method can detect multi-scale ships in different scenes of SAR images with extremely high accuracy and outperforms other ship detection methods implemented on SSDD.