In this paper, we focus on named entity boundary detection, which aims to detect the start and end boundaries of an entity mention in text, without predicting its type. A more accurate and robust detection approach is desired to alleviate error propagation in downstream applications, such as entity linking and fine-grained typing systems. Here, we first develop a novel entity boundary labeling approach with pointer networks, where the output dictionary size depends on the input, which is variable. Furthermore, we propose AT-Bdry, which incorporates adversarial transfer learning into an end-to-end sequence labeling model to encourage domain-invariant representations. More importantly, AT-Bdry can reduce domain difference in data distributions between the source and target domains, via an unsupervised transfer learning approach (i.e., no annotated target-domain data is necessary). We conduct Formal Text to Formal Text, Formal Text to Informal Text and ablation evaluations on five benchmark datasets. Experimental results show that AT-Bdry achieves state-of-the-art transferring performance against recent baselines.