In recent years, deep learning has found widespread application in SAR image object detection. However, when detecting multi-scale targets against complex backgrounds, these models often struggle to strike a balance between accuracy and speed. Furthermore, there is a continuous need to enhance the performance of current models. Hence, this paper proposes LRMSNet, a new multi-scale target detection model designed specifically for SAR images in complex backgrounds. Firstly, the paper introduces an attention module designed to enhance contextual information aggregation and capture global features, which is integrated into a backbone network with an expanded receptive field for improving SAR image feature extraction. Secondly, this paper develops an information aggregation module to effectively fuse different feature layers of the backbone network. Lastly, to better integrate feature information at various levels, this paper designs a multi-scale aggregation network. We validate the effectiveness of our method on three different SAR object detection datasets (MSAR-1.0, SSDD, and HRSID). Experimental results demonstrate that LRMSNet achieves outstanding performance with a mean average accuracy (mAP) of 95.2%, 98.9%, and 93.3% on the MSAR-1.0, SSDD, and HRSID datasets, respectively, with only 3.46 M parameters and 12.6 G floating-point operation cost (FLOPs). When compared with existing SAR object detection models on the MSAR-1.0 dataset, LRMSNet achieves state-of-the-art (SOTA) performance, showcasing its superiority in addressing SAR detection challenges in large-scale complex environments and across various object scales.