The non-factoid question answering system (QAS) responds to an input question by fetching an answer from a question answering (QA) database. The existing non-factoid QASs still cannot well adapt to specific professional domains due to the lack of domain knowledge. Aiming at this problem, this paper proposes a domain-specific non-factoid QAS by combining information retrieval technique and deep neural network. First, it extracts professional terms from the domain-specific documents. The professional terms can be used as an important source of domain knowledge. Second, it trains a deep Siamese neural network for semantically matching the questions. Finally, it queries and ranks the candidate answers based on the professional terms and the deep Siamese neural network. We conducted experiments based on two real domain-specific QA databases, and the experiment results have demonstrated the effectiveness of the proposed QAS.