With the recent growth of mobile communication, location-based services (LBSs) are getting much attention. While LBSs provide beneficial information about points of interest (POIs) such as restaurants or cafes near users, their current location could be revealed to the server. Lien et al. have recently proposed a privacy-preserving k-nearest neighbor (k-NN) search with additive homomorphic encryption. However, it requires heavy computation due to unnecessary multiplication in the encryption domain and this causes intolerant burden on the server. In this paper, we propose a lightweight private circular query protocol (LPCQP) for privacy-preserving k-NN search with additive and multiplicative homomorphism. Our proposed scheme divides a POI-table into some sub-tables and aggregates them with homomorphic cryptography in order to remove unnecessary POI information for the request user, and thus the computational cost required on the server is reduced. We evaluate the performance of our proposed scheme and show that our scheme reduces the computational cost on the LBS server while keeping high security and high accuracy.