The mobile phone has become a necessity in our life. Location based services have been able to be served in various devices such as mobile phone as well as car and deeply penetrated our life. Online social networks such as Facebook, Google, and Foursquare also incorporates various services using location information. However, these services need to be protected from exposure and misuse of location information while maintaining their usefulness and convenience. We propose a privacy-preserving location proximity protocol for location privacy based on fully homomorphic encryption without a trusted third party in a single round trip. Our proposed scheme can grasp the proximity of each other without exposing location information or distance. When one party requests the location of another party, our protocol uses homomorphic encryption to test if one party is within another's policy. Our main contribution is to provide a fully location privacy-preserving in one round trip with fixed computation time/amount without a trust third party.