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In recent years, the rapid development of Deep Learning (DL) has provided a new method for ship detection in Synthetic Aperture Radar (SAR) images. However, there are still four challenges in this task. (1) The ship targets in SAR images are very sparse. A large number of unnecessary anchor boxes may be generated on the feature map when using traditional anchor-based detection models, which could greatly increase the amount of computation and make it difficult to achieve real-time rapid detection. (2) The size of the ship targets in SAR images is relatively small. Most of the detection methods have poor performance on small ships in large scenes. (3) The terrestrial background in SAR images is very complicated. Ship targets are susceptible to interference from complex backgrounds, and there are serious false detections and missed detections. (4) The ship targets in SAR images are characterized by a large aspect ratio, arbitrary direction and dense arrangement. Traditional horizontal box detection can cause non-target areas to interfere with the extraction of ship features, and it is difficult to accurately express the length, width and axial information of ship targets. To solve these problems, we propose an effective lightweight anchor-free detector called R-Centernet+ in the paper. Its features are as follows: the Convolutional Block Attention Module (CBAM) is introduced to the backbone network to improve the focusing ability on small ships; the Foreground Enhance Module (FEM) is used to introduce foreground information to reduce the interference of the complex background; the detection head that can output the ship angle map is designed to realize the rotation detection of ship targets. To verify the validity of the proposed model in this paper, experiments are performed on two public SAR image datasets, i.e., SAR Ship Detection Dataset (SSDD) and AIR-SARShip. The results show that the proposed R-Centernet+ detector can detect both inshore and offshore ships with higher accuracy than traditional models with an average precision of 95.11% on SSDD and 84.89% on AIR-SARShip, and the detection speed is quite fast with 33 frames per second.