This study proposes a SAR(Synthetic Aperture Radar) image aircraft target recognition algorithm based on improved YOLOv5 for the small target and multi-scale detection problems in the fine-grained detection of aircraft targets in Synthetic Aperture Radar (SAR) images. First, a small target detection layer is added to solve the leakage detection problem of small targets and improve the target localization accuracy. Second, the polarized self-attention mechanism is introduced into the neck network, and the Bi-directional Feature Pyramid Network (BiFPN) is used for multilayer feature band-weight fusion to improve the attention to the scattering information of aircraft targets. Finally, SIoU (SCYLLA Intersection over Union, SIOU) is used as the network loss function to improve the convergence speed. In this paper, the effectiveness of the algorithm is tested by using the SAR-AIRcraft 1.0 dataset, and the improved YOLOv5 achieves 92.6% recall, 84.1% precision, and 90.1% mAP0.5. Experimental results show that the proposed algorithm has higher detection accuracy than other mainstream one-stage algorithms.