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Providing random access function in peer-to-peer on-demand video streaming is a challenging task, due to not only the asynchronous user interactivity but also the unpredictability of group dynamics. In this paper, we propose VMesh, a distributed peer-to-peer video-on-demand (VoD) streaming scheme which efficiently supports random seeking functionality. In VMesh, videos are divided into segments and stored in peers in a distributed manner. An overlay mesh is built upon peers to support jumping forward/backward, pause and restart during playback. Our scheme utilizes the large total storage capacity of peers to improve the segment supply so as to support interactive commands in a scalable manner. Through simulation, we show that our system outperforms a recent work, P2VoD. VMesh also has low segment missing rate under random member join/leave. In addition, the system achieves low joining and seeking latencies which are crucial requirements in an interactive VoD system.