In a kind of spatiotemporal database applications, objects move on the road networks. To process the position information for such kind of moving objects, people have proposed some index models, but they all have their limitations. These models are unable to index both the present and past positions of moving objects. Meanwhile, they only support window query or trajectory query. A new indexing technique which is called indexing moving objects trajectories on fixed networks (IMTFN) is proposed in this paper. IMTFN consists of a 2-dimensional (2D) R\+*-Tree for managing the fixed networks, a forest of 1-dimensional (1D) R\+*-Trees indexing the time interval for managing the position of moving objects, and a hash structure for the newest location of moving objects. IMTFN supports the efficient query of the present and past positions of moving objects, optimizes operations of windows query and trajectory query. Extensive experiments are conducted to evaluate the performance of the proposed indexing mechanism and show that IMTFN performs considerably better than STR-Tree and FNR-Tree.