Top-k queries are attractive for users in P2P systems with very large numbers of peers but difficult to support efficiently. In this paper, we propose a fully distributed algorithm for executing Top-k queries in the context of the APPA (Atlas Peer-to-Peer Architecture) data management system. APPA has a network-independent architecture that can be implemented over various P2P networks. Our algorithm requires no global information, does not depend on the existence of certain peers and its bandwidth cost is low. We validated our algorithm through implementation over a 64-node cluster and simulation using the BRITE topology generator and SimJava. Our performance evaluation shows that our algorithm has logarithmic scale up and improves Top-k query response time very well using P2P parallelism in comparison with baseline algorithms.