Domain adaptive person Re-Identification (ReID) is challenging owing to the domain gap and shortage of annotations on target scenarios. To handle those two challenges, this paper proposes a coupling optimization method including the Domain-Invariant Mapping (DIM) method and the Global-Local distance Optimization (GLO), respectively. Different from previous methods that transfer knowledge in two stages, the DIM achieves a more efficient one-stage knowledge transfer by mapping images in labeled and unlabeled datasets to a shared feature space. GLO is designed to train the ReID model with unsupervised setting on the target domain. Instead of relying on existing optimization strategies designed for supervised training, GLO involves more images in distance optimization, and achieves better robustness to noisy label prediction. GLO also integrates distance optimizations in both the global dataset and local training batch, thus exhibits better training efficiency. Extensive experiments on three large-scale datasets, i.e., Market-1501, DukeMTMC-reID, and MSMT17, show that our coupling optimization outperforms state-of-the-art methods by a large margin. Our method also works well in unsupervised training, and even outperforms several recent domain adaptive methods.