Cross-domain few-shot classification (CD-FSC) aims to identify novel target classes with a few samples, assuming that there exists a domain shift between source and target domains. Existing state-of-the-art practices typically pre-train on source domain and then finetune on the few-shot target data to yield task-adaptive representations. Despite promising progress, these methods are prone to overfitting the limited target distribution since data-scarcity and ignore the transferable knowledge learned in the source domain. To alleviate this problem, we propose a simple plug-and-play Adaptive Semantic Consistency (ASC) framework, which improves cross-domain robustness by preserving source transfer capability during the finetuning stage. Concretely, we reuse the source images in the pretraining phase and design an adaptive weight assignment strategy to highlight the samples similar to target domain, aiming to aggregate informative target-related knowledge from source domain. Subsequently, a semantic consistency regularization is applied to constrain the consistency between the semantic features of the source images output by the source model and target model. In this way, the proposed ASC enables explicit transfer of source domain knowledge to prevent the model from overfitting the target domain. Extensive experiments on multiple benchmarks demonstrate the effectiveness of the proposed ASC, and ASC provides consistent improvements over the baselines. The source code will be released.