In order to search similar moving object trajectories, the previously used methods focused on Euclidean distance and considered only spatial similarity. Euclidean distance is not appropriate for road network space, where the distance is limited to the space adjacent to the roads. In this paper, we consider the properties of moving objects in road network space and define temporal similarity as well as spatio-temporal similarity between trajectories based on POI (Points of Interest) and TOI (Times of Interest) on road networks. Based on these definitions, we propose methods for searching for similar trajectories in road network space. Experimental results show the accuracy of our methods and the average search time in query processing.