This paper studies the task of Visual Question Answering (VQA), which is topical in Multimedia community recently. Particularly, we explore two critical research problems existed in VQA: (1) efficiently fusing the visual and textual modalities; (2) enabling the visual reasoning ability of VQA models in answering complex questions. To address these challenging problems, a novel Question Guided Modular Routing Networks (QGMRN) has been proposed in this paper. Particularly, The QGMRN is composed of visual, textual and routing network. The visual and textual network serve as the backbones for the generic feature extractors of visual and textual modalities. QGMRN can fuse the visual and textual modalities at multiple semantic levels. Typically, the visual reasoning is facilitated by the routing network in a discrete and stochastic way by using Gumbel-Softmax trick for module selection. When the input reaches a certain modular layer, routing network newly proposed in this paper, dynamically selects a portion of modules from that layer to process the input depending on the question features generated by the textual network. It can also learn to reason by routing between the generic modules without additional supervision information or expert knowledge. Benefiting from the dynamic routing mechanism, QGMRN can outperform the previous classical VQA methods by a large margin and achieve the competitive results against the state-of-the-art methods. Furthermore, attention mechanism is integrated into our QGMRN model and thus can further boost the model performance. Empirically, extensive experiments on the CLEVR and CLEVR-Humans datasets validate the effectiveness of our proposed model, and the state-of-the-art performance has been achieved.