Closest point determination is a fundamental problem that arises in location-based services. In this paper, we study privacy-preserving closest point determination problem involving at least three parties, which focuses on determining the closest point without revealing location information. First, we present a three-party integer comparison protocol using homomorphic encryption systems in order to achieve the ciphertext comparison. Second, we propose a three-party and a multi-party protocol based on the integer comparison protocol to determine the closest point and prove that they are secure against semi-honest adversaries in the standard model. The proposed protocols are built on partially homomorphic encryption systems and can keep location and distance confidential. Finally, we confirm that our protocols reach a better balance between complexity and security. And experimental results demonstrate that our protocol is feasible and effective.