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Due to the rapid development of chip technology and deep learning revolution, many ship detection frameworks for synthetic aperture radar (SAR) imagery based on convolutional neural networks (CNNs) have been proposed and achieved great success. However, there are problems hampering their development: 1) For the SAR ship detection task, it is uneconomic to apply heavy backbone network to extract features because it results in heavy computing load and prolongs the inference time cost; 2) The anchor-based methods usually have massive hyper-parameters, which typically need to be tuned carefully and easily lead to weak detection performance. To alleviate the problems, an efficient low-cost ship detection network for SAR imagery is proposed in this paper. Firstly, a simplified U-Net as the backbone to extract features is proposed. It only contains ~0.47 million learnable weights, which is 2.37%, 0.76%, 0.34%, 1.01%, 0.55% and 1.07% of DarkNet-19, DarkNet-53, VGG-16, ResNet-50, ResNet-101 and ResNext-101, respectively. Secondly, an anchor-free SAR ship detection framework consisting of a bounding boxes regression sub-net and a score map regression sub-net based on simplified U-Net is proposed. To evaluate the effectiveness of our method, extensive experiments have been conducted and a more comprehensive set of evaluation metrics have been applied. Results demonstrate that the proposed network achieves 68.1% average precision and 67.6% average recall on the SAR ship detection dataset (SSDD), respectively. Compared with the state-of-the-art works, our proposed network achieves very competitive detection performance and extreme lightweight (~0.93 million learnable weights in total).