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This paper addresses the problem of natural language video localization (NLVL). Almost all existing works follow the "only look once" framework that exploits a single model to directly capture the complex cross- and self-modal relations among video-query pairs and retrieve the relevant segment. However, we argue that these methods have overlooked two indispensable characteristics of an ideal localization method: 1) Frame-differentiable: considering the imbalance of positive/negative video frames, it is effective to highlight positive frames and weaken negative ones during the localization. 2) Boundary-precise: to predict the exact segment boundary, the model should capture more fine-grained differences between consecutive frames since their variations are often smooth. To this end, inspired by how humans perceive and localize a segment, we propose a two-step human-like framework called Skimming-Locating-Perusing (SLP). SLP consists of a Skimming-and-Locating (SL) module and a Bi-directional Perusing (BP) module. The SL module first refers to the query semantic and selects the best matched frame from the video while filtering out irrelevant frames. Then, the BP module constructs an initial segment based on this frame, and dynamically updates it by exploring its adjacent frames until no frame shares the same activity semantic. Experimental results on three challenging benchmarks show that our SLP is superior to the state-of-the-art methods and localizes more precise segment boundaries.