In this study, we propose a method of unsupervised domain adaptive person re-identification. Given a labeled source-domain training set and an unlabeled target-domain training set, we explore how to improve the generalization ability of the person re-identification model on the target-domain test set. For this purpose, during the training of the model, the source-domain and target-domain training sets are simultaneously input into the model for training. While extracting global features, we extract local features to describe the person images and learn more fine-grained features. Furthermore, we apply Long Short-Term Memory (LSTM) for the modeling of a person in an end-to-end manner, treating the person as a sequence of body parts from the head to feet. Specifically, the method in this paper mainly includes two steps: (1) StarGAN is adopted to enhance the data of unlabeled target domain images; (2) the data sets of source domain and target domain are input into global branch and LSTM-based local branch at the same time for joint training. Finally, on the Market-1501 and DukeMTMC-reID data sets, the proposed model has achieved sound performance, which fully reflects its effectiveness.