In this paper, we address a novel task, namely weakly-supervised spatio-temporally grounding natural sentence in video. Specifically, given a natural sentence and a video, we localize a spatio-temporal tube in the video that semantically corresponds to the given sentence, with no reliance on any spatio-temporal annotations during training. First, a set of spatiotemporal tubes, referred to as instances, are extracted from the video. We then encode these instances and the sentence using our proposed attentive interactor which can exploit their fine-grained relationships to characterize their matching behaviors. Besides a ranking loss, a novel diversity loss is introduced to train the proposed attentive interactor to strengthen the matching behaviors of reliable instance-sentence pairs and penalize the unreliable ones. Moreover, we also contribute a dataset, called VID-sentence, based on the Im-ageNet video object detection dataset, to serve as a benchmark for our task. Extensive experimental results demonstrate the superiority of our model over the baseline approaches. Our code and the constructed VID-sentence dataset