Supporting relational query processing or dealing with spatial objects in peer-to-peer(P2P) data management systems needs multi-attribute exact match query processing and multi-attribute range query processing. A scheme to support these queries in P2P data management systems is proposed. By using a multi-attribute order-preserving hash mapping based on a virtual partition tree and indexing the generated keys of the multi-attribute data using P-Grid, data are partitioned dynamically among the dynamic set of peers. After that, a multi-attribute exact match query algorithm and two multi-attribute range query algorithms based on this partitioning strategy are proposed. Finally, two load balancing mechanisms are designed to ensure load balancing when the scheme works in a situation where data distribution in the multi-attribute data space is extremely skewed. Initial analysis shows that this work is effective and efficient.