Person re-identification (Re-ID) has achieved great success in the supervised scenario. However, it is difficult to directly transfer the supervised model to arbitrary unseen domains due to the model overfitting to the seen source domains. In this paper, we aim to tackle the generalizable multi-source person Re-ID task (i.e., there are multiple available source domains, and the testing domain is unseen during training) from the data augmentation perspective, thus we put forward a novel method, termed MixNorm. It consists of domain-aware mix-normalization (DMN) and domain-aware center regularization (DCR). Different from the conventional data augmentation, the proposed domain-aware mix-normalization enhances the diversity of features during training from the normalization perspective of the neural network, which can effectively alleviate the model overfitting to the source domains, so as to boost the generalization capability of the model in the unseen domain. To further promote the efficacy of the proposed DMN, we exploit the domain-aware center regularization to better map the diversely generated features into the same space. Extensive experiments on multiple benchmark datasets validate the effectiveness of the proposed method and show that the proposed method can outperform the state-of-the-art methods. Besides, further analysis also reveals the superiority of the proposed method.