Multi-modal video question answering aims to predict correct answer and localize the temporal boundary relevant to the question. The temporal annotations of questions improve QA performance and interpretability of recent works, but they are usually empirical and costly. To avoid the temporal annotations, we devise a weakly supervised question grounding (WSQG) setting, where only QA annotations are used and the relevant temporal boundaries are generated according to the temporal attention scores. To substitute the temporal annotations, we transform the correspondence between frames and subtitles to Frame-Subtitle (FS) self-supervision, which helps to optimize the temporal attention scores and hence improve the video-language understanding in VideoQA model. The extensive experiments on TVQA and TVQA+ datasets demonstrate that the proposed WSQG strategy gets comparable performance on question grounding, and the FS self-supervision helps improve the question answering and grounding performance on both QA-supervision only and full-supervision settings.