For the detection of marine ship objects in radar images, large-scale networks based on deep learning are difficult to be deployed on existing radar-equipped devices. This paper proposes a lightweight convolutional neural network, LiraNet, which combines the idea of dense connections, residual connections and group convolution, including stem blocks and extractor modules. The designed stem block uses a series of small convolutions to extract the input image features, and the extractor network adopts the designed two-way dense connection module, which further reduces the network operation complexity. Mounting LiraNet on the object detection framework Darknet, this paper proposes Lira-you only look once (Lira-YOLO), a lightweight model for ship detection in radar images, which can easily be deployed on the mobile devices. Lira-YOLO's prediction module uses a two-layer YOLO prediction layer and adds a residual module for better feature delivery. At the same time, in order to fully verify the performance of the model, mini-RD, a lightweight distance Doppler domain radar images dataset, is constructed. Experiments show that the network complexity of Lira-YOLO is low, being only 2.980 Bflops, and the parameter quantity is smaller, which is only 4.3 MB. The mean average precision (mAP) indicators on the mini-RD and SAR ship detection dataset (SSDD) reach 83.21{%} and 85.46{%}, respectively, which is comparable to the tiny-YOLOv3. Lira-YOLO has achieved a good detection accuracy with less memory and computational cost.