Person re-identification (ReID) has achieved great improvement under supervised settings, but suffers from considerable degradation when large distribution shifts between training and testing sets exist. Domain generalization (DG ReID) emerges to promote the generalization ability of models, overcoming the distribution shifts issue between source domains and unseen target domains. Among most prior methods in DG ReID, instance normalization (IN) serves as a promising solution for removing domain-specific information, however, it damages the discriminative ability simultaneously. In this article, we propose a new normalization method called Cluster-Instance Normalization (CINorm) to extract information from clusters for information compensation. The relations between samples in a batch can be mined to establish evolving clusters with aggregated samples during the forward training process. In this way, high intra-cluster congregation can eliminate the impacts of outliers to avoid overfitting, and high inter-cluster variances can synthesize diverse novel statistics to compensate discriminative information. Therefore, a Relation-Aware Normalization (RANorm) with a Dynamic ReCalibration (DRC) module is designed to integrate normalized features between evolving clusters and instances efficiently. Furthermore, a novel Group-based Triplet (G-Triplet) loss is proposed to divide a batch into multiple groups with greater compactness for hard-pair mining. Extensive experiments show that our method outperforms state-of-the-art algorithms on multiple DG benchmarks by a large margin. The proposed method can also achieve superior performance on image classification tasks under DG settings without using domain labels.