Recently, methods based on deep learning have been successfully applied to ship detection for synthetic aperture radar (SAR) images. However, most current ship detection networks rely too much on the anchor mechanism. These methods have low accuracy and poor generalization ability for multiscale ship detection. To solve the aforementioned problems, an anchor-free framework for multiscale ship detection in SAR images based on a balance attention network (BANet) is proposed. First, due to the diversity of scales and rotation angles of ships, deformable convolution is introduced to build a local attention module (LAM) to better obtain local information of ships and effectively enhance the robustness of the network. Second, a nonlocal attention module (NLAM) is designed to extract the nonlocal features of the SAR image, so as to balance the local features and nonlocal features acquired by the entire network. Finally, the feature pyramid network (FPN) is used to detect ships of different sizes at different scales. The detection results on three datasets demonstrate that the detection precision of our method is higher than that of all comparison methods, and this method achieves the most advanced performance.