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Though P2P grid has attracted great attention these days, trust management is still a complex and difficult task. This paper proposes a dynamic reputation management framework to enhance trust in the unstructured P2P Grid. The proposed model extends the normal trust model and takes the impact of the mobility of peers into account. Based on this framework, we show how to calculate, store, collect and query reputation values in an accurate and efficient manner. Simulation experiments show that significant performance gains can be gotten using this framework.