Abstract This research strives for natural language moment retrieval in long, untrimmed video streams. The problem is not trivial especially when a video contains multiple moments of interests and the language describes complex temporal dependencies, which often happens in real scenarios. We identify two crucial challenges: semantic misalignment and structural misalignment. However, existing approaches treat different moments separately and do not explicitly model complex moment-wise temporal relations. In this paper, we present Moment Alignment Network (MAN), a novel framework that unifies the candidate moment encoding and temporal structural reasoning in a single-shot feed-forward network. MAN naturally assigns candidate moment representations aligned with language semantics over different temporal locations and scales. Most importantly, we propose to explicitly model moment-wise temporal relations as a structured graph and devise an iterative graph adjustment network to jointly learn the best structure in an end-to-end manner. We evaluate the proposed approach on two challenging public benchmarks DiDeMo and Charades-STA, where our MAN significantly outperforms the state-of-the-art by a large margin.