Video watching time is a crucial measure for studying user watching behavior in online Internet video-on-demand (VoD) systems. It is important for system planning, user engagement study, and service quality evaluation. However, due to limited access to large-scale VoD systems, there is still a lack of accurate model for characterizing the distribution of user watching time on a per video basis. In this paper, we measure PPLive, one of the most popular commercial Internet VoD systems in China, over a three week period, and characterize user watching time distributions of 1,000 most popular movies. We find that a video's watching time can be modeled by a concatenation of exponential distribution (in the first several minutes of the video) and truncated power law distribution (in the remaining time of the video), when users watch the video without interruptions. For comparison, user watching time with user interactions such as seeking and/or pause operations does not follow such a distribution. We further reveal interesting characteristics regarding the relation between video's watching time distribution and various watching/video-related features (including time-of-day, user ratings, and movie genres). Our measurement and modeling results bring forth important insights for design, deployment, and evaluation of Internet VoD systems.