Modern search engines usually provide a query language with a set of advanced syntactic operators (e.g., plus sign to require a term's appearance, or quotation marks to require a phrase's appearance) which if used appropriately, can significantly improve the effectiveness of a plain keyword query. However, they are rarely used by ordinary users due to the intrinsic difficulties and users' lack of corpora statistics. In this paper, we propose to automatically reformulate queries that do not work well by selectively adding syntactic operators. Particularly, we propose to perform syntactic operator-based query reformulation when a retrieval system detects users encounter difficulty in search as indicated by users' behaviors such as scanning over top k documents without click-through. We frame the problem of automatic reformulation with syntactic operators as a supervised learning problem, and propose a set of effective features to represent queries with syntactic operators. Experiment results verify the effectiveness of the proposed method and its applicability as a query suggestion mechanism for search engines. As a negative feedback strategy, syntactic operator-based query reformulation also shows promising results in improving search results for difficult queries as compared with existing methods.