The focus of this paper is on how to use the parallel dataflow technique to optimize and process queries on parallel databases. A set of algorithms for implementing the query optimizers of parallel database systems based on the parallel dataflow technique, such as the algorithms for generating parallel dataflow graph from a query, the algorithms for processor assignment, and the algorithms for scheduling and executing the parallel query plan, are proposed. A parallel query optimizer using the algorithms are presented also in the paper. The algorithms and the optimizer have been used in a prototype parallel database system designed by the author. It is shown that the proposed algorithms and the optimizer are very efficient and effective for optimizing and processing queries on parallel databases.