Because of the rapid growth of mobile communication and wireless communication, Location-based services are handled in many applications. So, the management and analysis of spatio-temporal data are a hot issue in database research. Index structure and query processing of such contents are very important for these applications. This paper addressees algorithms that make index structure by using Douglas-Peucker Algorithm and process nearest neighbor search query efficiently on moving objects trajectories. We compare and analyze our algorithms by experiments. Our algorithms make small size of index structure and process the query more efficiently.