The rapid development of mobile computing and technologies such as RFID and GPS, has led to the generation of massive temporal and spatial data; demand to process this data has increased. Due to this trend, a growing number of researchers are interested in analyzing the trajectories of moving objects. Many methods have been proposed to solve this problem. In particular, Baltzer et al [1] proposed a new Group-By operator GROUP TRAJECTORIES for analyzing trajectories, which is implemented by three computing group methods: Group By Overlap, Group By Intersection, and Group By Overlap and Intersection. The purpose of this research is to expand upon Baltzer et al's methods by improving the results of computing groups of trajectories, trying to optimize parameters and simplifying the usage of the Group-By operator. The Shifting Grid Algorithm and Auto Parameters Algorithm are proposed for improving computing group results, and applied for both Group By Intersection and Group By Overlap. The Group By Intersection is intended for parallel movement of moving objects. Group By Overlap is desirable for the analysis of sequences of movements. The Shifting Grid Algorithm and Auto Parameters Algorithm can improve the resulting groups of trajectory computation for both cases in data sets with and without noise. The Auto Parameters Algorithm is proposed for improving the result combined with the Shifting Grid Algorithm, automatically calculated groups of trajectories, and determined a better result according to the de