Existing deep learning algorithms for synthetic aperture radar (SAR) image recognition are performed with offline data. These methods must use all data to retrain the entire model when new data are added. However, facing the real application environment with growing data, retraining consumes much time and memory space. Class-Incremental Learning (CIL) addresses this problem that deep learning faces in streaming data. The goal of CIL is to enable the model to continuously learn new classes without using all data to retrain the model while maintaining the ability to recognize previous classes. Most of the CIL methods adopt a replay strategy to realize it. However, the number of retained samples is too small to carry enough information. The replay strategy is still trapped by forgetting previous knowledge. For this reason, we propose a CIL method for SAR images based on self-sustainment guidance representation. The method uses the vision transformer (ViT) structure as the basic framework. We add a dynamic query navigation module to enhance the model’s ability to learn the new classes. This module stores special information about classes and uses it to guide the direction of feature extraction in subsequent model learning. In addition, the method also comprises a structural extension module to defend the forgetting of old classes when the model learns new knowledge. It is constructed to maintain the representation of the model in previous classes. The model will learn under the coordinated guidance of old and new information. Experiments on the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset show that our method performs well with remarkable advantages in CIL tasks. This method has a better accuracy rate and performance dropping rate than state-of-the-art methods under the same setting and maintains the ability of incremental learning with fewer replay samples. Additionally, experiments on a popular image dataset (CIFAR100) also demonstrate the scalability of our approach.