When adding new tasks/classes in an incremental learning scenario, the previous recognition capabilities trained on the previous training data can be lost. In the real-life application of automatic target recognition (ATR), part of the previous samples may be able to be used. Most incremental learning methods have not considered how to save the previous key samples. In this article, the class boundary exemplar selection-based incremental learning (CBesIL) is proposed to save the previous recognition capabilities in the form of the class boundary exemplars. For exemplar selection, the class boundary selection method based on local geometrical and statistical information is proposed. And when adding new classes continually, a class-boundary-based data reconstruction method is introduced to update the exemplar set. Thus, when adding new classes, the previous class boundaries could be kept complete. Experimental results demonstrate that the proposed CBesIL outperforms the other state of the art on the accuracy of multiclass recognition and class-incremental recognition.