With the supervision from source domain only in class-level, existing unsupervised domain adaption (UDA) methods mainly learn the domain-invariant representations from a shared feature extractor, which cause the source-bias problem. This paper proposes an unsupervised domain adaption approach with Teacher-Student Competition (TSC). In particular, a student network is introduced to learn the target-specific feature space, and we design a novel competition mechanism to select more credible pseudo-labels for the training of student network. We introduce a teacher network with the structure of existing conventional UDA method, and both teacher and student networks compete to provide target pseudo-labels to constrain every target sample's training in student network. Extensive experiments demonstrate that our proposed TSC framework significantly outperforms the state-of-the-art domain adaption methods on Office-31 and ImageCLEF-DA benchmarks.