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Multimodal machine translation (MMT), which mainly focuses on enhancing text-only translation with visual features, has attracted considerable attention from both computer vision and natural language processing communities. Most current MMT models resort to attention mechanism, global context modeling or multimodal joint representation learning to utilize visual features. However, the attention mechanism lacks sufficient semantic interactions between modalities while the other two provide fixed visual context, which is unsuitable for modeling the observed variability when generating translation. To address the above issues, in this paper, we propose a novel Dynamic Context-guided Capsule Network (DCCN) for MMT. Specifically, at each timestep of decoding, we first employ the conventional source-target attention to produce a timestep-specific source-side context vector. Next, DCCN takes this vector as input and uses it to guide the iterative extraction of related visual features via a context-guided dynamic routing mechanism. Particularly, we represent the input image with global and regional visual features, we introduce two parallel DCCNs to model multimodal context vectors with visual features at different granularities. Finally, we obtain two multimodal context vectors, which are fused and incorporated into the decoder for the prediction of the target word. Experimental results on the Multi30K dataset of English-to-German and English-to-French translation demonstrate the superiority of DCCN. Our code is available on https://github.com/DeepLearnXMU/MM-DCCN.