Synthetic aperture radar (SAR) ship classification is of great significance in the field of maritime observation. On one hand, how to comprehensively utilize the amplitude and phase information in SAR data has become a key problem for improving the performance of ship classification. On the other hand, there is a lack of available complex-valued SAR databases for the purpose of classification. To solve the above problems, a complex-valued SAR deep learning model, FDC-TA-DSN, based on four-dimensional dynamic convolution (FDC) and triple attention (TA) mechanism, is proposed. First, this new deep SAR-Net (DSN) devises an FDC module to reduce the influence of SAR speckle noise and enhance the adaptability of the network for inputting features, and a TA module to suppress background sea clutter and capture important features. Second, joint time-frequency analysis was used to obtain the radar spectrogram of SAR data, and the stacked convolutional autoencoder was used to learn the phase information of SAR data to obtain the backscattering characteristics. Finally, the two kinds of information are formed into fusion features for learning to improve the classification accuracy. To support this investigation, a complex-valued SAR dataset ComplexSAR_Ship is constructed for the first time by using the two high-resolution modes of UFS and FSI of the Gaofen-3 satellite. The dataset includes 17 ship types with nearly 3000 high-resolution ship slices. The experimental results show that, compared with the current popular networks, such as DSN, ResNet, VGG, etc., FDC-TA-DSN has achieved better performance, and the network has good generalization ability in SAR data classification.