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Domain adaptive person re-identification (re-ID) is a challenging task due to the large discrepancy between the source domain and the target domain. To reduce the domain discrepancy, existing methods mainly attempt to generate pseudo labels for unlabeled target images by clustering algorithms. However, clustering methods tend to bring noisy labels and the rich fine-grained details in unlabeled images are not sufficiently exploited. In this paper, we seek to improve the quality of labels by capturing feature representation from multiple augmented views of unlabeled images. To this end, we propose a Self-Supervised Knowledge Distillation (SSKD) technique containing two modules, the identity learning and the soft label learning. Identity learning explores the relationship between unlabeled samples and predicts their one-hot labels by clustering to give exact information for confidently distinguished images. Soft label learning regards labels as a distribution and induces an image to be associated with several related classes for training peer network in a self-supervised manner, where the slowly evolving network is a core to obtain soft labels as a gentle constraint for reliable images. Finally, the two modules can resist label noise for re-ID by enhancing each other and systematically integrating label information from unlabeled images. Extensive experiments on several adaptation tasks demonstrate that the proposed method outperforms the current state-of-the-art approaches by large margins.