Person re-identification (Re-ID) aims to match identities across non-overlapping camera views. Researchers have proposed many supervised Re-ID models which require quantities of cross-view pairwise labelled data. This limits their scalabilities to many applications where a large amount of data from multiple disjoint camera views is available but unlabelled. Although some unsupervised Re-ID models have been proposed to address the scalability problem, they often suffer from the view-specific bias problem which is caused by dramatic variances across different camera views, e.g., different illumination, viewpoints and occlusion. The dramatic variances induce specific feature distortions in different camera views, which can be very disturbing in finding cross-view discriminative information for Re-ID in the unsupervised scenarios, since no label information is available to help alleviate the bias. We propose to explicitly address this problem by learning an unsupervised asymmetric distance metric based on cross-view clustering. The asymmetric distance metric allows specific feature transformations for each camera view to tackle the specific feature distortions. We then design a novel unsupervised loss function to embed the asymmetric metric into a deep neural network, and therefore develop a novel unsupervised deep framework named the DEep Clustering-based Asymmetric MEtric Learning (DECAMEL). In such a way, DECAMEL jointly learns the feature representation and the unsupervised asymmetric metric. DECAMEL learns a compact cross-view cluster structure of Re-ID data, and thus help alleviate the view-specific bias and facilitate mining the potential cross-view discriminative information for unsupervised Re-ID. Extensive experiments on seven benchmark datasets whose sizes span several orders show the effectiveness of our framework.