Synthetic aperture radar (SAR) image detection often encounters problems such as error sensitivity and high computational complexity, which pose challenges to SAR target recognition. Researchers have proposed many novel and efficient deep learning methods for SAR data. However, most of these deep learning networks for SAR target recognition use the same methods as optical real-valued processing, directly applying real-valued deep neural networks to SAR images. Real-valued neural networks to some extent lose the phase information, which cannot fully utilize the complex characteristics of SAR data. As phase information is a unique data feature in SAR images, it plays a crucial role in applications such as SAR interferometry, information retrieval, and target recognition. In order to make the network more suitable for extracting complex data features from SAR, breaking the architecture of traditional neural networks, this paper proposes a novel end-to-end fully complex-valued multi-stage convolutional neural network (Complex-valued mUltI-Stage convolutIonal Neural nEtworks, CUISINE) architecture. It realizes the computation in the full complex-valued domain from the input of SAR complex image data to convolutional calculations, and finally to classification labels. Experimental comparisons on the publicly available MSTAR dataset show that our method performs well in SAR target classification. The accuracy reaches 99.42% on the test set with a phase error of 0 rad, and 88.05% on the test set with a phase error of 50 rad. © 2024 Chinese Institute of Electronics. All rights reserved.