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Query-based video grounding is an important yet challenging task in video understanding, which aims to localize the target segment in an untrimmed video according to a sentence query. Most previous works achieve significant progress by addressing this task in a fully-supervised manner with segment-level labels, which require high labeling cost. Although some recent efforts develop weakly-supervised methods that only need the video-level knowledge, they generally match multiple pre-defined segment proposals with query and select the best one, which lacks fine-grained frame-level details for distinguishing frames with high repeatability and similarity within the entire video. To alleviate the above limitations, we propose a self-contrastive learning framework to address the query-based video grounding task under a weakly-supervised setting. Firstly, instead of utilizing redundant segment proposals, we propose a new grounding scheme that learns frame-wise matching scores referring to the query semantic to predict the possible foreground frames by only using the video-level annotations. Secondly, since some predicted frames (i.e., boundary frames) are relatively coarse and exhibit similar appearance to their adjacent frames, we propose a coarse-to-fine contrastive learning paradigm to learn more discriminative frame-wise representations for distinguishing the false positive frames. In particular, we iteratively explore multi-scale hard negative samples that are close to positive samples in the representation space for distinguishing fine-grained frame-wise details, thus enforcing more accurate segment grounding. Extensive experiments on two challenging benchmarks demonstrate the superiority of our proposed method compared with the state-of-the-art methods.