Equipped with mobile devices, people relied on location-based services can expediently and reasonably organize their activities. But location information may disclose people's sensitive information, such as interests, health status. Besides, the limited resources of mobile devices restrict the further development of location-based services. In this paper, aiming at the fair meeting position determination service, we design a lightweight privacy-preserving solution. In our scheme, mobile users only need to submit service requests. A cloud server and a location services provider are responsible for service response, where the cloud server achieves most of the calculation, and the location services provider determines the fair meeting location based on the computational results of the cloud server and broadcasts it to mobile users. The proposed scheme adopts homomorphic encryptions and random permutation methods to preserve the location privacy of mobile users. The security analyses show that the proposed scheme is privacy-preserving under our defined threat models. Besides, the presented solution only needs to calculate n Euclidean distances, and hence, our scheme has linear computation and communication complexity.