Abstract: LSZ is a heterogeneous distributed database system based on different LANs, different microcomputers and different DBMSs It provides a uniform interface through a global relational data language GRDL to data in heterogeneous distributed databases This paper presents the query optimization strategies of LSZ which contains semantic query optimization based on heuristic rules and parallel multi-join optimization. The semantic optimizer transforms a query into a semantically equivalent query that is less expensive than the original query, while the multi-join optimizer takes both communication cost and parallelism into account for processing the transformed query.