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Peer-to-Peer(P2P) network has some closer relation-ship with Internet while the scale of P2P network increases. Active P2P worms attack neighbour peers based on hit-list and pose a severe threat to both P2P network and Internet. Due to the complexity of P2P network, the traditional worms propagation model cannot be adequate to exact model P2P worms spread. Both the dynamic characteristic of P2P network and the heterogeneity of peers could have some great impact on active P2P worms spread. A mathematical model of active P2P worms propagation is presented in this paper. We simulate active P2P worms spread after analyzing the mathematical model. The results show that many factors could affect the propagation of active P2P worms such as the state of P2P network, the scan rate of P2P worms, and the security knowledge peers have. We also study the late phase of active P2P worms spread and find that a very small space of P2P network is enough to guarantee active P2P worms self-propagation when peers cannot repair security holes in time for many reasons.