Unsupervised person re-identification (Re-Id) has attracted increasing attention due to its practical application in the read-world video surveillance system. The traditional unsupervised Re-Id are mostly based on the method alternating between clustering and fine-tuning with the classification or metric learning objectives on the grouped clusters. However, since person Re-Id is an open-set problem, the clustering based methods often leave out lots of outlier instances or group the instances into the wrong clusters, thus they can not make full use of the training samples as a whole. To solve these problems, we present the hybrid dynamic cluster contrast and probability distillation algorithm. It formulates the unsupervised Re-Id problem into an unified local-to-global dynamic contrastive learning and self-supervised probability distillation framework. Specifically, the proposed method can make the best of the self-supervised signals of all the clustered and un-clustered instances, from both the instances' self-contrastive level and the probability distillation respectives, in the memory-based non-parametric manner. Besides, the proposed hybrid local-to-global contrastive learning can take full advantage of the informative and valuable training examples for effective and robust training. Extensive experiment results show that the proposed method achieves superior performances to state-of-the-art methods, under both the purely unsupervised and unsupervised domain adaptation experiment settings. Our source code is released in https://github.com/zjy2050/HDCRL-ReID.