Referring image segmentation aims at segmenting out the object or stuff referred to by a natural language expression. The challenge of this task lies in the requirement of understanding both vision and language. The linguistic structure of a referring expression can provide an intuitive and explainable layout for reasoning over visual and linguistic concepts. In this paper, we propose a structured attention network (SANet) to explore the multimodal reasoning over the dependency tree parsed from the referring expression. Specifically, SANet implements the multimodal reasoning using an attentional multimodal tree-structure recurrent module (AMTreeGRU) in a bottom-up manner. In addition, for spatial detail improvement, SANet further incorporates the semantics-guided low-level features into high-level ones using the proposed attentional skip connection module. Extensive experiments on four public benchmark datasets demonstrate the superiority of our proposed SANet with more explainable visualization examples.