In this study, we first investigate a novel capsule network with dynamic routing for linear time Neural Machine Translation (NMT), referred as \textsc{CapsNMT}. \textsc{CapsNMT} uses an aggregation mechanism to map the source sentence into a matrix with pre-determined size, and then applys a deep LSTM network to decode the target sequence from the source representation. Unlike the previous work \cite{sutskever2014sequence} to store the source sentence with a passive and bottom-up way, the dynamic routing policy encodes the source sentence with an iterative process to decide the credit attribution between nodes from lower and higher layers. \textsc{CapsNMT} has two core properties: it runs in time that is linear in the length of the sequences and provides a more flexible way to select, represent and aggregates the part-whole information of the source sentence. On WMT14 English-German task and a larger WMT14 English-French task, \textsc{CapsNMT} achieves comparable results with the state-of-the-art NMT systems. To the best of our knowledge, this is the first work that capsule networks have been empirically investigated for sequence to sequence problems.