A hybrid P2P system, such as Napster, has a central directory where the peers publish information about the content they offer for sharing. We study the incentives for self-interested node?s participating in such P2P system with centralized directory, by developing the new cost model of P2P network. In our model, a node will participate the system if and only if it can get more than it gives. We discover several interesting conclusions on the character of the participating. There is probably a threshold value in such P2P systems, that is, the system is unstable when the number of its nodes is less than the threshold and the system is stable and self-developing when its size exceeding the thresh-old.