In the field of machine learning, hyperbolic space demonstrates superior representation capabilities for hierarchical data compared to conventional Euclidean space. This work focuses on the Coarse-To-Fine Few-Shot Class-Incremental Learning (C2FSCIL) task. Our study follows the Knowe approach, which contrastively learns coarse class labels and subsequently normalizes and freezes the classifier weights of learned fine classes in the embedding space. To better interpret the "coarse-to-fine" paradigm, we propose embedding the feature extractor into hyperbolic space. Specifically, we employ the Poincaré ball model of hyperbolic space, enabling the feature extractor to transform input images into feature vectors within the Poincaré ball instead of Euclidean space. We further introduce hyperbolic contrastive loss and hyperbolic fully-connected layers to facilitate model optimization and classification in hyperbolic space. Additionally, to enhance performance under few-shot conditions, we implement maximum entropy distribution in hyperbolic space to estimate the probability distribution of fine-class feature vectors. This allows generation of augmented features from the distribution to mitigate overfitting during training with limited samples. Experiments on C2FSCIL benchmarks show that our method effectively improves both coarse and fine class accuracies.