Using the principle of imitation learning and the theory of optimal transport we propose in this paper a novel model for unsupervised domain adaptation named Teacher Imitation Domain Adaptation with Optimal Transport (TIDOT). Our model includes two cooperative agents: a teacher and a student. The former agent is trained to be an expert on labeled data in the source domain, whilst the latter one aims to work with unlabeled data in the target domain. More specifically, optimal transport is applied to quantify the total of the distance between embedded distributions of the source and target data in the joint space, and the distance between predictive distributions of both agents, thus by minimizing this quantity TIDOT could mitigate not only the data shift but also the label shift. Comprehensive empirical studies show that TIDOT outperforms existing state-of-the-art performance on benchmark datasets.