In this paper, we propose a system model for querying and indexing the GPS trajectory of moving objects on PostGIS/PostgreSQL. We developed moving object data types including MPoint(moving point), MDouble(moving double) for GPS trajectories. Also, various moving objects UDFs(user-defined functions) are implemented for moving objects queries. For efficient query processing, r-tree index is extended for trajectory, and pre-materialization techniques are proposed for fast UDF processing. Experimental results show that the pre-materialization techniques are about 1.2 times faster than naïve query processing using r-tree index.