The R-trees are usually used for an index of trajectories in moving-objects databases. However, they need to access a number of nodes to trace same trajectories because of considering only a spatial proximity. Overlaps and dead spaces should be minimized to enhance the performance of range queries in moving-objects indexes. Trajectories of moving-objects should be preserved to enhance the performance of the trajectory queries. In this paper, we propose the TP3DR-tree(Trajectory Preserved 3DR-tree) using clusters of trajectories for range and trajectory queries. The TP3DR-tree uses two split policies: one is a spatial splitting that splits the same trajectory by clustering and the other is a time splitting that increases space utilization. In addition, we use connecting information in non-leaf nodes to enhance the performance of combined-queries. Our experiments show that the new index outperforms the others in processing queries on various datasets.