Incomplete utterance rewriting has recently raised wide attention. However, previous works do not consider the semantic structural information between incomplete utterance and rewritten utterance or model the semantic structure implicitly and insufficiently. To address this problem, we propose a QUEry-Enhanced Network (QUEEN). Firstly, our proposed query template explicitly brings guided semantic structural knowledge between the incomplete utterance and the rewritten utterance making model perceive where to refer back to or recover omitted tokens. Then, we adopt a fast and effective edit operation scoring network to model the relation between two tokens. Benefiting from proposed query template and the well-designed edit operation scoring network, QUEEN achieves state-of-the-art performance on several public datasets.