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Multimodal named entity recognition (MNER) is a critical step in information extraction, which aims to detect entity spans and classify them to corresponding entity types given a sentence-image pair. Existing methods either (1) obtain named entities with coarse-grained visual clues from attention mechanisms, or (2) first detect fine-grained visual regions with toolkits and then recognize named entities. However, they suffer from improper alignment between entity types and visual regions or error propagation in the two-stage manner, which finally imports irrelevant visual information into texts. In this paper, we propose a novel end-to-end framework named MNER-QG that can simultaneously perform MRC-based multimodal named entity recognition and query grounding. Specifically, with the assistance of queries, MNER-QG can provide prior knowledge of entity types and visual regions, and further enhance representations of both texts and images. To conduct the query grounding task, we provide manual annotations and weak supervisions that are obtained via training a highly flexible visual grounding model with transfer learning. We conduct extensive experiments on two public MNER datasets, Twitter2015 and Twitter2017. Experimental results show that MNER-QG outperforms the current state-of-the-art models on the MNER task, and also improves the query grounding performance.