The rapid advancement of hypersonic targets presents significant challenges to aerospace defense systems. Recognition methods based on multi-band radiation spectral features offer a promising solution for hypersonic vehicle identification. However, existing techniques struggle with the incremental recognition of new target classes and are vulnerable to catastrophic forgetting. To address these limitations, this paper introduces the Incremental DenseNet and Spectral Angle Learning Method (IDSALM) for hypersonic target incremental recognition. IDSALM combines DenseNet-based feature extraction with dynamic classification optimization, utilizing the Dynamic Adaptive Spectral Angle Classifier (DASA-Classifier) to address intraclass variability and interclass ambiguity through spectral angle metrics, dynamically adapting to changes in target distributions. The Selective Retention and Exemplar Management (SREM) module mitigates catastrophic forgetting and improves model update efficiency through knowledge replay and selection of representative exemplars. In the four-stage incremental experiments, with the addition of two new classes per stage, IDSALM achieves an Average Accuracy (AA) exceeding 94% and a Kappa coefficient surpassing 0.93, significantly reducing recognition confusion and catastrophic forgetting compared to alternative methods. Furthermore, IDSALM improves model update efficiency, reducing the update time to just 3.74% of that of non-incremental methods. These results demonstrate IDSALM’s efficiency and robustness, establishing a solid technological foundation for space-based multi-band spectral recognition of hypersonic targets.