How to build a high-quality multi-domain dialogue system is a challenging work due to its complicated and entangled dialogue state space among each domain, which seriously limits the quality of dialogue policy, and further affects the generated response. In this paper, we propose a novel method to acquire a satisfying policy and subtly circumvent the knotty dialogue state representation problem in the multi-domain setting. Inspired by real school teaching scenarios, our method is composed of multiple domain-specific teachers and a universal student. Each individual teacher only focuses on one specific domain and learns its corresponding domain knowledge and dialogue policy based on a precisely extracted single domain dialogue state representation. Then, these domain-specific teachers impart their domain knowledge and policies to a universal student model and collectively make this student model a multi-domain dialogue expert. Experiment results show that our method reaches competitive results with SOTAs in both multi-domain and single domain setting.