For a peer-to-peer (P2P) system holding massive amount of data, efficient semantic based search for resources (such as data or services) is a key determinant to its scalability. This paper presents the design of an overlay network, namely semantic small world (SSW), that facilitates efficient semantic based search in P2P systems. SSW is based on three innovative ideas: 1) small world network; 2) semantic clustering; 3) dimension reduction. Peers in SSW are clustered according to the semantics of their local data and self-organized as a small world overlay network. To address the maintenance issue of high dimensional overlay networks, a dynamic dimension reduction method, called adaptive space linearization, is used to construct a one-dimensional SSW that supports operations in the high dimensional semantic space. SSW achieves a very competitive trade-off between the search latencies/traffic and maintenance overheads. Through extensive simulations, we show that SSW is much more scalable to very large network sizes and very large numbers of data objects compared to pSearch, the state-of-the-art semantic-based search technique for P2P systems. In addition, SSW is adaptive to distribution of data and locality of interest; is very resilient to failures; and has good load balancing property.