In the past few years, language-based video retrieval has attracted a lot of attention. However, as a natural extension, localizing the specific video moments within a video given a description query is seldom explored. Although these two tasks look similar, the latter is more challenging due to two main reasons: 1) The former task only needs to judge whether the query occurs in a video and returns an entire video, but the latter is expected to judge which moment within a video matches the query and accurately returns the start and end points of the moment. Due to the fact that different moments in a video have varying durations and diverse spatial- temporal characteristics, uncovering the underlying moments is highly challenging. 2) As for the key component of relevance estimation, the former usually embeds a video and the query into a common space to compute the relevance score. However, the later task concerns moment localization where not only the features of a specific moment matter, but the context information of the moment also contributes a lot. For example, the query may contain temporal constraint words, such as “first”, therefore temporal context is required to properly comprehend them.To address these issues, we develop an Attentive Cross-Modal Retrieval Network. In particular, we design a memory attention mechanism to emphasize the visual features mentioned in the query and simultaneously incorporate their context. In the light of this, we obtain an augmented moment representation. Meanwhile, a cross-modal fusion sub-network learns both the intra-modality and inter-modality dynamics, which can enhance the learning of moment-query representation. We evaluate our method on two datasets: DiDeMo and TACoS. Extensive experiments show the effectiveness of our model as compared to state-of-the-art methods.