Developing Video-Grounded Dialogue Systems (VGDS), where a dialogue is conducted based on visual and audio aspects of a given video, is significantly more challenging than traditional image or text-grounded dialogue systems because (1) feature space of videos span across multiple picture frames, making it difficult to obtain semantic information; and (2) a dialogue agent must perceive and process information from different modalities (audio, video, caption, etc.) to obtain a comprehensive understanding. Most existing work is based on RNNs and sequence-to-sequence architectures, which are not very effective for capturing complex long-term dependencies (like in videos). To overcome this, we propose Multimodal Transformer Networks (MTN) to encode videos and incorporate information from different modalities. We also propose query-aware attention through an auto-encoder to extract query-aware features from non-text modalities. We develop a training procedure to simulate token-level decoding to improve the quality of generated responses during inference. We get state of the art performance on Dialogue System Technology Challenge 7 (DSTC7). Our model also generalizes to another multimodal visual-grounded dialogue task, and obtains promising performance. We implemented our models using PyTorch and the code is released at https://github.com/henryhungle/MTN.