Massive amounts of video data are ubiquitously generated in personal devices and dedicated video recording facilities. Analyzing such data would be extremely beneficial in real world (e.g., urban traffic analysis, pedestrian behavior analysis, video surveillance). However, videos contain considerable sensitive information, such as human faces, identities and activities. Most of the existing video sanitization techniques simply obfuscate the video by detecting and blurring the region of interests (e.g., faces, vehicle plates, locations and timestamps) without quantifying and bounding the privacy leakage in the sanitization. In this paper, to the best of our knowledge, we propose the first differentially private video analytics platform (VideoDP) which flexibly supports different video analyses with rigorous privacy guarantee. Different from traditional noise-injection based differentially private mechanisms, given the input video, VideoDP randomly generates a utility-driven private video in which adding or removing any sensitive visual element (e.g., human, object) does not significantly affect the output video. Then, different video analyses requested by untrusted video analysts can be flexibly performed over the utility-driven video while ensuring differential privacy. Finally, we conduct experiments on real videos, and the experimental results demonstrate that our VideoDP effectively functions video analytics with good utility.