With the wide availability of mobile devices (smart phones, iPhones, etc.), mobile locationbased queries are increasingly in demand. One of the most frequent queries is range search which returns objects of interest within a pre-defined area. Most of the existing methods are based on the road network expansion method -expanding all nodes (intersections and objects) and computing the distance of each node to the query point. Since road networks are extremely complex, node expansion approaches are inefficient. In this paper, we propose a method, Voronoi Range Search (VRS) based on the Voronoi diagram, to process range search queries efficiently and accurately by partitioning the road networks to some special polygons. Then we further propose Voronoi Continuous Range (VCR) to satisfy the requirement for continuous range search queries (moving queries) based on VRS. Our empirical experiments show that VRS and VCR surpass all their rivals for both static and moving queries.