Although natural language question answering over knowledge graphs have been studied in the literature, existing methods have some limitations in answering complex questions. To address that, in this paper, we propose a State Transition-based approach to translate a complex natural language question N to a semantic query graph (SQG), which is used to match the underlying knowledge graph to find the answers to question N. In order to generate SQG, we propose four primitive operations (expand, fold, connect and merge) and a learning-based state transition approach. Extensive experiments on several benchmarks (such as QALD, WebQuestions and ComplexQuestions) with two knowledge bases (DBpedia and Freebase) confirm the superiority of our approach compared with state-of-the-arts.