Exemplar-free class-incremental learning (EFCIL) presents a significant challenge, requiring models to learn tasks sequentially without accessing data from previous tasks. This challenge is exacerbated when the initial dataset is insufficient for facilitating model adaptation to subsequent tasks. Existing methods often employ a joint loss function to improve model adaptability and knowledge retention. However, these methods still face challenges in mitigating forgetting of knowledge from old classes. To address this issue, we propose a new approach called Adaptive Knowledge Matching (AKM). We first adopt a log-cosh loss function to better retain previously learned knowledge. Then, we introduce an adaptive weighting strategy that dynamically balances knowledge from old and new classes. Experiments on benchmark datasets (CIFAR100, Tiny-ImageNet, and ImageNet-Subset) demonstrate the effectiveness of the proposed approach.