The goal of electronic monitoring of longline fishing is to visually monitor the fish catching activities on fishing vessels based on cameras, either for regulatory compliance or catch counting. The previous hierarchical classification method demonstrates efficient fish species identification of catches from longline fishing, where fishes are under severe deformation and self-occlusion during the catching process. Although the hierarchical classification mitigates the laborious efforts of human reviews by providing confidence scores in different hierarchical levels, its performance drops dramatically under the class incremental learning (CIL) scenario. A CIL system should be able to learn about more and more classes over time from a stream of data, i.e., only the training data for a small number of classes have to be present at the beginning and new classes can be added progressively. In this work, we introduce a Hierarchical Class Incremental Learning (HCIL) model, which significantly improves the state-of-the-art hierarchical classification methods under the CIL scenario.