Prototypical Network is a popular few-shot solver that aims at establishing a feature metric generalizable to novel few-shot classification (FSC) tasks using deep neural networks. However, its performance drops dramatically when generalizing to the FSC tasks in new domains. In this study, we revisit this problem and argue that the devil lies in the simplicity bias pitfall in neural networks. In specific, the network tends to focus on some biased shortcut features (e.g., color, shape, etc.) that are exclusively sufficient to distinguish very few classes in the meta-training tasks within a pre-defined domain, but fail to generalize across domains as some desirable semantic features. To mitigate this problem, we propose a Local-global Distillation Prototypical Network (LDP-net). Different from the standard Prototypical Network, we establish a two-branch network to classify the query image and its random local crops, respectively. Then, knowledge distillation is conducted among these two branches to enforce their class affiliation consistency. The rationale behind is that since such global-local semantic relationship is expected to hold regardless of data domains, the local-global distillation is beneficial to exploit some cross-domain transferable semantic features for feature metric establishment. Moreover, such local-global semantic consistency is further enforced among different images of the same class to reduce the intra-class semantic variation of the resultant feature. In addition, we propose to update the local branch as Exponential Moving Average (EMA) over training episodes, which makes it possible to better distill cross-episode knowledge and further enhance the generalization performance. Experiments on eight cross-domain FSC benchmarks empirically clarify our argument and show the state-of-the-art results of LDP-net. Code is available in https://github.com/NWPUZhoufei/LDP-Net