Cross-domain transfer learning (CDTL) is an extremely challenging task for the person re-identification (ReID). Given a source domain with annotations and a target domain without annotations, CDTL seeks an effective method to transfer the knowledge from the source domain to the target domain. However, such a simple two-domain transfer learning method is unavailable for the person ReID in that the source/target domain consists of several sub-domains, e.g., camera-based sub-domains. To address this intractable problem, we propose a novel Many-to-Many Generative Adversarial Transfer Learning method (M2M-GAN) that takes multiple source sub-domains and multiple target sub-domains into consideration and performs each sub-domain transferring mapping from the source domain to the target domain in a unified optimization process. The proposed method first translates the image styles of source sub-domains into that of target sub-domains, and then performs the supervised learning by using the transferred images and the corresponding annotations in source domain. As the gap is reduced, M2M-GAN achieves a promising result for the cross-domain person ReID. Experimental results on three benchmark datasets Market-1501, DukeMTMC-reID and MSMT17 show the effectiveness of our M2M-GAN.