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Multiscale object detection in Synthetic Aperture Radar (SAR) images can locate and recognize key objects in large-scene SAR images, and it is one of the key technologies in SAR image interpretation. However, for the simultaneous detection of SAR objects with large size differences, that is, cross-scale object detection, existing object detection methods are difficult to extract the features of cross-scale objects, and also difficult to realize cross-scale object simultaneous detection. In this study, we propose a multiscale object detection method based on the Feature-Transferable Pyramid Network (FTPN) for SAR images. In the feature extraction stage, the feature migration method is used to obtain an effective mosaic of the feature images of each layer and extract feature images with different scales. Simultaneously, the void convolution method is used to increase the receptive field of feature extraction and aid the network in extracting large object features. These steps can effectively preserve the features of objects of different sizes, to realize the simultaneous detection of cross-scale objects in SAR images. The experiments based on the GaoFen-3 SAR dataset, SAR Ship Detection Dataset (SSDD), and high-resolution SSDD-2.0 show that the proposed method can detect cross-scale objects, such as airports and ships in SAR images, and the mean Average Precision (mAP) can reach 96.5% on the existing dataset, which is 8.1% higher than that of the characteristic pyramid network algorithm. Moreover, the overall performance of the proposed method is better than that of the latest YOLOv4 and other object detection algorithms.