Referring Expression Comprehension (REC) aims to localize the target objects specified by free-form natural language descriptions in images. While state-of-the-art methods achieve impressive performance, they perform dense perception of images, which incorporates redundant visual regions unrelated to linguistic queries, leading to additional computational overhead. This inspires us to explore a question: can we eliminate linguistic-irrelevant redundant visual regions to improve the efficiency of the model ? Existing relevant methods primarily focus on fundamental visual tasks, with limited exploration in vision-language fields. To address this, we propose a coarse-to-fine iterative perception framework, called ScanFormer. It can iteratively exploit the image scale pyramid to extract linguistic-relevant visual patches from top to bottom. In each iteration, irrelevant patches are discarded by our designed informativeness prediction. Furthermore, we propose a patch selection strategy for discarded patches to accelerate inference. Experiments on widely used datasets, namely RefCOCO, RefCOCO+, RefCOCOg, and ReferItGame, verify the effectiveness of our method, which can strike a balance between accuracy and efficiency.