In the Vehicular Ad-hoc Networks (VANETs), a vehicle or the vehicle driver could be recognized and tracked by eavesdropping its queries (e.g., beacons) by an adversary as these contains personal information like location, speed, and communication of the vehicles. This attack leads to threats to the vehicle`s location and leakage of personal information. The current solution, is to use the anonymizer as a third trusted party between the vehicles and the LBS. In this paper we refer to the use of a Fog server with Fog anonymizer to secure the communication among the vehicles and LBS. Our scheme consists of four phases. In first phase, the vehicle driver initiates the communication process and generate the encrypted messages. These messages may contain the sub-messages. In phase 2, the Fog server received the messages via different roots. The Fs combined the messages and decrypt the messages based on the PK received by the vehicle. All the Fog server perform the same task for encryption and decryption. If any of the Fog server was compromised, we still had the link for communication. In Phase 3, the Fog anonymizer receive the messages from the Fog node, anonymize them based on the anonymization process. Thereafter, the Fog anonymizer send these messages to LBS to achieve desired goals. The Fog anonymizer perform the same job for anonymization and de-anonymization, while sending and receiving the messages from the LBS. In the last phase, the LBS received the messages from the Fog anonymizer, understand the communication messages, compile the desired results, and sent them back to the Fog anonymizer. Our analysis shows that the proposed scheme preserved the location privacy based on the queries at low communication and computational cost.