Peer-to-peer (P2P) systems have become a popular platform for sharing and exchanging voluminous information among thousands or even millions of users. The massive amount of information shared in such systems mandates efficient semantic-based search instead of key-based search. The majority of existing proposals can only support simple key-based search rather than semantic-based search. This paper presents the design of an overlay network, namely, semantic small world (SSW), that facilitates efficient semantic-based search in P2P systems. SSW achieves the efficiency based on four ideas: 1) semantic clustering, where peers with similar semantics organize into peer clusters, 2) dimension reduction, where to address the high maintenance overhead associated with capturing high-dimensional data semantics in the overlay, peer clusters are adaptively mapped to a one-dimensional naming space, 3) small world network, where peer clusters form into a one-dimensional small world network, which is search efficient with low maintenance overhead, and 4) efficient search algorithms, where peers perform efficient semantic-based search, including approximate point query and range query in the proposed overlay. Extensive experiments using both synthetic data and real data demonstrate that SSW is superior to the state of the art on various aspects, including scalability, maintenance overhead, adaptivity to distribution of data and locality of interest, resilience to peer failures, load balancing, and efficiency in support of various types of queries on data objects with high dimensions.