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Recent advances in person re-identification (ReID) obtain impressive accuracy in the supervised and unsupervised learning settings. However, most of the existing methods need to train a new model for a new domain by accessing data. Due to public privacy, the new domain data are not always accessible, leading to a limited applicability of these methods. In this paper, we study the problem of multi-source domain generalization in ReID, which aims to learn a model that can perform well on unseen domains with only several labeled source domains. To address this problem, we propose the Memory-based Multi-Source Meta-Learning (M$^3$L) framework to train a generalizable model for unseen domains. Specifically, a meta-learning strategy is introduced to simulate the train-test process of domain generalization for learning more generalizable models. To overcome the unstable meta-optimization caused by the parametric classifier, we propose a memory-based identification loss that is non-parametric and harmonizes with meta-learning. We also present a meta batch normalization layer (MetaBN) to diversify meta-test features, further establishing the advantage of meta-learning. Experiments demonstrate that our M$^3$L can effectively enhance the generalization ability of the model for unseen domains and can outperform the state-of-the-art methods on four large-scale ReID datasets.