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The management of moving objects is an intensive study area in recent years. Currently many researches focus on objects freely moving on 2-dimensional space, and a lot of index strategies have been proposed, while they are not applicable for objects moving on fixed networks. As objects moving on fixed networks are pervasive in real application, its study is of great practical significance. As changing over time frequently is a main characteristic of moving objects' position, index strategies for moving objects' trajectories need to provide efficient dynamic updating ability besides high query performance. In this paper, we propose an efficient index strategy named Grid Partition R-Tree (GPR-Tree), for indexing trajectories of moving objects on fixed network. By dividing the network space into grids of different size and indexing trajectories in each grid, GPR-Tree provides efficient query as well as updating performance for moving objects' trajectories.