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Oriented to adaptive recognition of the new land-cover categories, incremental classification (IC) that aims to complete adaptive classification with continuous learning is urgent and crucial for hyperspectral image classification (HSIC). Nevertheless, deep-learning-based HSIC models adopted the learning paradigm with fixed classes yield unsatisfactory inference in the situation of IC due to the catastrophic forgetting problem. To eliminate the recognition gap and maintain the old knowledge during IC, in this article, we propose a novel approach called the distillation-constrained prototype representation network (DCPRN) for hyperspectral image IC (HSIIC). The primary goal of DCPRN is to enhance the discriminative capability for recognizing the original classes in HSIIC while effectively integrating both the original and the incremental knowledge to facilitate adaptive learning. Specifically, the proposed framework incorporates a prototype representation mechanism, which serves as a bridge for knowledge transfer and integration between the initial and incremental learning phases of HSIIC. In addition, we present a dual knowledge distillation (DKD) module in incremental learning, which integrates discriminative information at both the feature level (FL) and decision level (DL). In this way, the proposed mechanism enables flexible and dynamic adaptation to new classes and overcomes the limitations of fixed-category feature learning. Extensive experimental analysis conducted on three popular datasets validates the superiority of the proposed DCPRN method compared with other typical HSIIC approaches.