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The use of peer-to-peer (P2P) applications is growing dramatically. Most P2P applications use the routing algorithm that selecting the neighbor nodes at random. This routing algorithm increases the routing hops and reduces the routing speed. To get better routing speed with less routing hops, a new routing algorithm named RGAAC based on group-average agglomerative clustering was presented. Structured by k clusters topology, this P2P network has k cluster center nodes. The cluster center nodes ensure the high performance of the RGAAC. Compared to some other P2P overlay routing algorithms, the RGAAC increases the performance in routing efficiency. The conclusions show that the RGAAC is an efficient routing algorithm, but also has some problems waiting for further study.