Existing Few-Shot Learning (FSL) methods learn and recognize new classes with the help of prior knowledge. However, they cannot handle this task well in a cross-domain scenario when training and testing sets are from different domains, since the fact that prior knowledge in different domains often varies greatly. To solve this problem, in this paper, we propose a few-shot domain generalization method, which is designed to extract relationship embeddings using Forget-Update Modules named FUM. The relationship embedding considers valuable relational information between samples in a specific task, and the forget-update module takes into account differences between domains and adjusts the distribution of relational embeddings through forgetting and updating mechanisms based on specific tasks. To evaluate the few-shot domain generalization ability of FUM, extensive experiments on eight cross-domain scenarios and six same-domain scenarios are conducted, and the results show that FUM achieves superior performances compared to recent few-shot learning methods. Visualization results also show that the distribution of the relationship embeddings extracted by FUM has stronger few-shot domain generalization ability than the feature embeddings used in the existing FSL methods.