The rapid growth of user-generated videos on the Internet has intensified the need for text-based video retrieval systems. Traditional methods mainly favor the concept-based paradigm on retrieval with simple queries, which are usually ineffective for complex queries that carry far more complex semantics. Recently, embedding-based paradigm has emerged as a popular approach. It aims to map the queries and videos into a shared embedding space where semantically-similar texts and videos are much closer to each other. Despite its simplicity, it forgoes the exploitation of the syntactic structure of text queries, making it suboptimal to model the complex queries. To facilitate video retrieval with complex queries, we propose a Tree-augmented Cross-modal Encoding method by jointly learning the linguistic structure of queries and the temporal representation of videos. Specifically, given a complex user query, we first recursively compose a latent semantic tree to structurally describe the text query. We then design a tree-augmented query encoder to derive structure-aware query representation and a temporal attentive video encoder to model the temporal characteristics of videos. Finally, both the query and videos are mapped into a joint embedding space for matching and ranking. In this approach, we have a better understanding and modeling of the complex queries, thereby achieving a better video retrieval performance. Extensive experiments on large scale video retrieval benchmark datasets demonstrate the effectiveness of our approach. CCS CONCEPTS • Information systems → Multimedia and multimodal retrieval; Video search.