Supporting free VCR-like operations in P2P VoD streaming systems is challenging. The uncertainty of frequent VCR operations makes it difficult to provide high quality realtime streaming services over distributed self-organized P2P overlay networks. Recently, prefetching has emerged as a promising approach to smooth the streaming quality. However, how to efficiently and effectively prefetch suitable segments is still an open issue. In this paper, we propose PREP, a PREdiction-based Prefetching scheme to support VCR-like operations over gossip-based P2P on-demand streaming systems. By employing the reinforcement learning technique, PREP transforms users' streaming service procedure into a set of abstract states and presents an online prediction model to predict a user's VCR behavior via analyzing the large volumes of user viewing logs collected on the tracker. We further present a distributed data scheduling algorithm to proactively fetch segments according to the predicted VCR behavior. Moreover, PREP takes advantage of the inherent peer collaboration of gossip protocol to optimize the response latency. Through comprehensive simulations, we demonstrate the efficiency of PREP by gaining the accumulated hit ratio close to 75% while reducing the response latency close to 70% with only less than 15% extra stress on the server side.