The traditional synthetic aperture radar automatic target recognition (SAR/ATR) algorithm can train a sufficient number of known class samples and classify the samples in the test set. However, if the old model is trained only with the new class samples, the old class samples’ knowledge is easily forgotten by the new model, which is called catastrophic forgetting. The reason is that the model only fits the distribution of current training samples, so training the whole dataset is necessary. Due to the limitation of storage resources, it is often not feasible to retain the whole dataset. In order to avoid this phenomenon, a small number of old class samples can be kept to train with the new class samples. Therefore, how to select the old class samples becomes the key point. In this article, the density coverage-based exemplar selection (DCBES) is proposed to choose the key samples of the old class. DCBES selects samples based on the metric learning theory and the set covering theory. First, the metric learning theory is used to measure the similarity between samples and to obtain the density range of samples. Then, the exemplar selection problem is considered a set covering problem, to select a fixed number of exemplars to achieve the maximum coverage of the class density range. Experiments on the moving and stationary target acquisition and recognition (MSTAR) dataset show that our method is superior to other exemplar selection methods and achieves the best results.