Unsupervised person re-identification has been improved significantly by the development of cross domain person re-identification models, which apply useful knowledge in source data to completely unlabeled target data. However, existing cross domain re-identification models still remain a major limitation that they are all based on single-source and single-target setting. The only one source domain may remain a tremendous gap between target, generating negative effect for the model training in target domain. To overcome this drawback, this paper proposes a Multi-Source Transfer Network to learn a shared target-biased feature space between multi-source and target domains, which achieves transfer learning in feature-level, pixel-level, and task-level by the proposed target-biased multi-source transfer learning module, relativistic adversarial learning module, and task-gap bridging module, respectively. Through leveraging the domain gaps in feature-level, pixel-level, and task-level, this network can synthetically learn a discriminative model from multiple source domains to effectively conduct re-identification in target domain. Furthermore, this paper conducts extensive experiments on three widely-recognized person re-identification datasets, and the proposed network achieves rank-1 accuracies of 80.9% and 74.6% on DukeMTMC-reID and Market-1501 datasets, respectively. The results demonstrate the contribution of the proposed method, compared with state-of-the-art methods, including hand-crated feature, clustering and transfer learning based methods. INDEX TERMS Multi-source transfer, relativistic discriminator, cross domain, person re-identification.