Since only the spatial feature information of ship target is utilized, the current deep learning-based synthetic aperture radar (SAR) ship detection approaches cannot achieve a satisfactory performance, especially in the case of multiscale or rotations, and the complex background. To overcome these issues, a novel multidimensional domain deep learning network for SAR ship detection is developed in this work to exploit the spatial and frequency-domain complementary features. The proposed method consists of the following main three steps. First, to learn hierarchical spatial features, the feature pyramid network (FPN) is adopted to produce ship target spatial multiscale characteristics with a top-down structure. Second, with a polar Fourier transform, the rotation-invariant features of SAR ship targets are obtained in the frequency domain. After that, a novel spatial-frequency characteristics fusion network is then presented, which seeks to learn more compact feature representations across different domains by updating the parameters of sub-networks interactively. The detection results are obtained due to utilizing the multidimensional domain information, and we evaluate the effectiveness of the proposed method using the existing SAR ship detection data set (SSDD). The results of the proposed method outperform other convolutional neural network (CNN)-based algorithms, especially for multiscale and rotation ship targets under complex backgrounds.