The current limited spaceborne hardware resources and the diversity of ship target scales in SAR images have led to the requirement of on-orbit real-time detection of ship targets in spaceborne synthetic aperture radar (SAR) images. In this paper, we propose a lightweight ship detection network based on the YOLOv4-LITE model. In order to facilitate the network migration to the satellite, the method uses MobileNetv2 as the backbone feature extraction network of the model. To solve the problem of ship target scale diversity in SAR images, an improved receptive field block (RFB) structure is introduced, enhancing the feature extraction ability of the network, and improving the accuracy of multi-scale ship target detection. A sliding window block method is designed to detect the whole SAR image, which can solve the problem of image input. Experiments on the SAR ship dataset SSDD show that the detection speed of the improved lightweight network could reach up to 47.16 FPS, with the mean average precision (mAP) of 95.03%, and the model size is only 49.34 M, which demonstrates that the proposed network can accurately and quickly detect ship targets. The proposed network model can provide a reference for constructing a spaceborne real-time lightweight ship detection network, which can balance the detection accuracy and speed of the network.