With the spread of mobile devices and advances in communication techknowledges, the needs of application which uses the movement patterns of moving objects in history trajectory data of moving objects gets Increasing. Especially, to design public transportation route or road network of the new city, we can use the similar patterns in the trajectories of moving objects that move on the spatial network such as road and railway. In this paper, we propose a spatio-temporal similar trajectory search algorithm for moving objects on road network. For this, we define a spatio-temporal similarity measure based on the real road network distance and propose a grid-based index structure for similar trajectory search. Finally, we analyze the performance of the proposed similar trajectory search algorithm in order to show its efficiency.