Traditional constant false alarm rate (CFAR) based ship target detection methods do not work well in complex conditions, such as multi-scale situations or inshore ship detection. With the development of deep learning techniques, methods based on convolutional neural networks (CNN) have been applied to solve such issues and have demonstrated good performance. However, compared with optical datasets, the number of samples in SAR datasets is much smaller, thus limiting the detection performance. Moreover, most state-of-the-art CNN-based ship target detectors that focus on the detection performance ignore the computation complexity. To solve these issues, this paper proposes a lightweight densely connected sparsely activated detector (DSDet) for ship target detection. First, a style embedded ship sample data augmentation network (SEA) is constructed to augment the dataset. Then, a lightweight backbone utilizing a densely connected sparsely activated network (DSNet) is constructed, which achieves a balance between the performance and the computation complexity. Furthermore, based on the proposed backbone, a low-cost one-stage anchor-free detector is presented. Extensive experiments demonstrate that the proposed data augmentation approach can create hard SAR samples artificially. Moreover, utilizing the proposed data augmentation approach is shown to effectively improves the detection accuracy. Furthermore, the conducted experiments show that the proposed detector outperforms the state-of-the-art methods with the least parameters (0.7 M) and lowest computation complexity (3.7 GFLOPs).