A κ-Range Nearest Neighbor (or κRNN for short) query in road networks finds the κ nearest neighbors of every point on the road segments within a given query region based on the network distance. The κRNN query is significantly important for location-based applications in many realistic scenarios. For example, (1) the user's location is uncertain, i.e., user's location is modeled by a spatial region, and (2) the user is not willing to reveal her exact location to preserve her privacy, i.e., her location is blurred into a spatial region. However, the existing solutions for κRNN queries simply apply the traditional κ-nearest neighbor query processing algorithm multiple times, which poses a huge redundant searching overhead. To this end, we propose an efficient κRNN query processing algorithm in this paper. Our algorithm (1) employs a shared execution approach to eliminate the redundant searching overhead, and (2) provides a parameter that can be tuned to achieve a tradeoff between the query processing performance and the storage overhead, while guaranteeing the user's exact κ-nearest neighbors are included in the query answers. The experimental results show that our algorithm always outperforms the existing solution in terms of query response time, and the introduced tuning parameter is an effective way to achieve the tradeoff between the query response time and the storage overhead.