With the advances in wireless Internet and mobile positioning technology, location-based services (LBSs) have become popular. In LBSs, users must send their exact locations in order to use the services, but they may be subject to several privacy threats. To solve this problem, query processing algorithms based on a cloaking method have been proposed. The algorithms use spatial cloaking methods to blur the user's exact location in a region satisfying the required privacy threshold (k). With the cloaked region, an LBS server can execute a spatial query processing algorithm preserving their privacy. However, the existing algorithms cannot provide good query processing performance. To resolve this problem, we, in this paper, propose a k-NN query processing algorithm based on network Voronoi diagram for spatial networks. Therefore, our algorithm can reduce network expansion overhead and share the information of the expanded road network. In order to demonstrate the efficiency of our algorithms, we have conducted extensive performance evaluations. The results show that our algorithm achieves better performance on retrieval time than the existing algorithms, such as PSNN and kRNN. This is because our k-NN query processing algorithm can greatly reduce a network expansion cost for retrieving k POIs.