In domain-specific NER, due to insufficient labeled training data, deep models usually fail to behave normally. In this paper, we proposed a novel Neural Inductive TEaching framework (NITE) to transfer knowledge from existing domain-specific NER models into an arbitrary deep neural network in a teacher-student training manner. NITE is a general framework that builds upon transfer learning and multiple instance learning, which collaboratively not only transfers knowledge to a deep student network but also reduces the noise from teachers. NITE can help deep learning methods to effectively utilize existing resources (i.e., models, labeled and unlabeled data) in a small domain. The experiment resulted on Disease NER proved that without using any labeled data, NITE can significantly boost the performance of a CNN-bidirectional LSTM-CRF NER neural network nearly over 30% in terms of F1-score.