Knearest neighbor search is an important problem in location-based services and has been well studied on static road networks. However, in real world, road networks are often time-dependent; i.e., the time for traveling through a road always changes over time. Most existing methods forkNN query build various indexes maintaining the shortest distances for some pairs of vertices on static road networks. Unfortunately, these methods cannot be used for the time-dependent road networks because the shortest distances always change over time. To (...) address the problem ofkNN query on time-dependent road networks, we propose a novel voronoi-based index in this paper. Furthermore, we propose a novel balanced tree, namedV-tree, which is a secondary level index on voronoi-based index to make our querying algorithm more efficient. Moreover, we propose an algorithm for preprocessing time-dependent road networks such that the waiting time is not necessary to be considered. We confirm the efficiency of our method through experiments on real-life datasets. (shrink)