Recently, unsupervised domain adaptation in person re-identification (ReID) has been widely studied to improve the generalization ability of the ReID model. Some existing methods focus on handling the intra-domain image variations caused by different camera configurations, pose, illumination, and background in target domain. However, they fail to fully mine the underlying consistency constraints contained in unlabeled target dataset. To comprehensively investigate the underlying constraints for unsupervised representation learning, we introduce two consistency constraints to deal with the intra-domain variations, namely instance-ensembling consistency and crossgranularity consistency. Specifically, the instance-ensembling consistency constraint aims to encourage similar features for a given instance and its positive samples. The cross-granularity consistency constraint is designed to enhance the collaboration of global clues and local clues in multi-granularity feature learning, which can overcome the negative effects caused by the noisy pseudo labels. By combining the advantages of the two constraints, we propose an iterative Intra-domain Consistency Enhancement (ICE) approach based on the Mean Teacher framework to fully mine the two underlying consistency constraints on multigranularity features. The proposed ICE approach achieves significant improvement compared with the state-of-the-art, which demonstrates the superiority of the two consistency constraints.