In the increasingly complex electromagnetic environment, a variety of new signal types are appearing; however, existing electromagnetic signal classification (ESC) models cannot handle new signal types. In this context, the emergence of class-incremental learning aims to incrementally update the classification model as new categories emerge. In this paper, an electromagnetic signal classification framework based on class exemplar selection and a multi-objective linear programming classifier (CES-MOLPC) is proposed in order to continuously learn new classes in an incremental manner. Specifically, our approach involves the adaptive selection of class exemplars considering normalized mutual information and a multi-objective linear programming classifier. The former is used to maintain the classification capability of the model for previous categories by selecting key samples, while the latter is used to allow the model to adapt quickly to new categories. Meanwhile, a weighted loss function based on cross-entropy and distillation loss is presented in order to fine-tune the model. We demonstrate the effectiveness of the proposed CES-MOLPC method through extensive experiments on the public RML2016.04c data set and the large-scale real-world ACARS signal data set. The results of the comparative experiments demonstrate that our method can achieve significant improvements over state-of-the-art methods.