An multi-scale synthetic aperture radar （SAR） image detection algorithm for ships based on improved YOLOv5 is proposed to address the large pixel scale difference of ship targets in complex scenes and missed detection caused by dense array of ships. For the neck network of YOLOv5， a bi-directional feature pyramid network （BiFPN） is adopted to enhance the multi-scale feature fusion ability of the network， and an enhanced channel-MLP （EC-MLP） module is constructed based on depthwise separable convolution （DSC） and channel MLP in its bottom-up feature fusion branch to enrich semantic information and provide more sufficient ship target context features. The global attention mechanism （GAM） is introduced to enable the network to extract input features selectively and reduce information reduction. In addition， the SIoU loss function is used to further improve the training convergence speed and detection accuracy of the network. Comparative experiments with eight other methods （Faster R-CNN， Libra R-CNN， FCOS， YOLOv5s， PP-YOLOv2， YOLOX-s， PP-YOLOE-s and YOLOv7-tiny） are conducted on SSDD and HRSID datasets. The experimental results show that the AP50 of the improved algorithm reaches 96.7% on SSDD and 95.6% on HRSID， which is superior to the comparison methods.