Abstract: Visual Relational Reasoning is crucial for many vision-and-language based tasks, such as Visual Question Answering and Vision Language Navigation. In this paper, we consider reasoning on complex referring expression comprehension (c-REF) task that seeks to localise the target objects in an image guided by complex queries. Such queries often contain complex logic and thus impose two key challenges for reasoning: (i) It can be very difficult to comprehend the query since it often refers to multiple objects and describes complex relationships among them. (ii) It is non-trivial to reason among multiple objects guided by the query and localise the target correctly. To address these challenges, we propose a novel Modular Graph Attention Network (MGA-Net). Specifically, to comprehend the long queries, we devise a language attention network to decompose them into four types: basic attributes, absolute location, visual relationship and relative locations, which mimics the human language understanding mechanism. Moreover, to capture the complex logic in a query, we construct a relational graph to represent the visual objects and their relationships, and propose a multi-step reasoning method to progressively understand the complex logic. Extensive experiments on CLEVR-Ref+, GQA and CLEVR-CoGenT datasets demonstrate the superior reasoning performance of our MGA-Net.