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Unsupervised person re-identification (Re-ID) is a promising and very challenging research problem in computer vision. Learning robust and discriminative features with unlabeled data is of central importance to Re-ID. Recently, more attention has been paid to unsupervised Re-ID algorithms based on clustered pseudo-label. However, the previous approaches did not fully exploit information of hard samples, simply using cluster centroid or all instances for contrastive learning. In this paper, we propose a Hard-sample Guided Hybrid Contrast Learning (HHCL) approach combining cluster-level loss with instance-level loss for unsupervised person Re-ID. Our approach applies cluster centroid contrastive loss to ensure that the network is updated in a more stable way. Meanwhile, introduction of a hard instance contrastive loss further mines the discriminative information. Extensive experiments on two popular large-scale Re-ID benchmarks demonstrate that our HHCL outperforms previous state-of-the-art methods and significantly improves the performance of unsupervised person Re-ID. The code of our work is available soon at https://github.com/bupt-ai-cz/HHCL-ReID.