In this paper, we present a novel Motion-Attentive Transition Network (MATNet) for zero-shot video object segmentation, which provides a new way of leveraging motion information to reinforce spatio-temporal object representation. An asymmetric attention block, called Motion-Attentive Transition (MAT), is designed within a two-stream encoder, which transforms appearance features into motion-attentive representations at each convolutional stage. In this way, the encoder becomes deeply interleaved, allowing for closely hierarchical interactions between object motion and appearance. This is superior to the typical two-stream architecture, which treats motion and appearance separately in each stream and often suffers from overfitting to appearance information. Additionally, a bridge network is proposed to obtain a compact, discriminative and scale-sensitive representation for multi-level encoder features, which is further fed into a decoder to achieve segmentation results. Extensive experiments on three challenging public benchmarks (i.e., DAVIS-16, FBMS and Youtube-Objects) show that our model achieves compelling performance against the state-of-the-arts. Code is available at: https://github.com/tfzhou/MATNet.