It is crucial for query auto-completion to accurately predict what a user is typing. Given a query prefix and its context (e.g., previous queries), conventional context-aware approaches often produce relevant queries to the context. The purpose of this paper is to investigate the feasibility of exploiting the context to learn user reformulation behavior for boosting prediction performance. We first conduct an in-depth analysis of how the users reformulate their queries. Based on the analysis, we propose a supervised approach to query auto-completion, where three kinds of reformulationrelated features are considered, including term-level, querylevel and session-level features. These features carefully capture how the users change preceding queries along the query sessions. Extensive experiments have been conducted on the large-scale query log of a commercial search engine. The experimental results demonstrate a significant improvement over 4 competitive baselines.