Recent works show that mean-teaching is an effective framework for unsupervised domain adaptive person re-identification. However, existing methods perform contrastive learning on selected samples between teacher and student networks, which is sensitive to noises in pseudo labels and neglects the relationship among most samples. Moreover, these methods are not effective in cooperation of different teacher networks. To handle these issues, this paper proposes a Graph Consistency based Mean-Teaching (GCMT) method with constructing the graph consistency constraint between teacher and student networks. Specifically, given unlabeled training images, we apply teacher networks to extract corresponding features and further construct a teacher graph for each teacher network to describe the similarity relationships among training images. To boost the representation learning, different teacher graphs are fused to provide the supervise signal for optimizing student networks. GCMT fuses similarity relationships predicted by different teacher networks as supervision and effectively optimizes student networks with more sample relationships involved. Experiments on three datasets, i.e., Market-1501, DukeMTMCreID, and MSMT17, show that proposed GCMT outperforms state-of-the-art methods by clear margin. Specially, GCMT even outperforms the previous method that uses a deeper backbone. Experimental results also show that GCMT can effectively boost the performance with multiple teacher and student networks. Our code is available at this https URL .