Inter-vehicle communication is one of the most important parts in Intelligent Vehicle System. Through this communication, drivers can recognize what is happening out of their sights, such as the freezing condition of the street, traffic accidents, and so on. Each car in IVS gives various services to the drivers after analyzing those received information from cars or a base station. If the message is, however, exchanged from car to car directly, the computation cost which is needed for all the car to authenticate the transmitted message between nearby cars is tremendously high. Therefore, one can naturally think that the message communication between cars is performed with the help of the base station to reduce the computation cost. In this case where the base station collects all the information transmitted from cars and broadcasts them nearby, there should be an efficient way both for the base station to authenticate the car message within its communication range and for the car to authenticate the information received from the base station. In this paper, we present a two-way authentication protocol using a hash chain to efficiently exchange GPS information between a car and a base station. This information can be used to provide a driver with the navigation which displays all the moving cars around him in real time. When a car goes into an area of a base station, the car authenticates itself to the base station using its private key of PKI, sends a commitment of a hash chain, then starts to send a message with the hash value for authentication. The message includes GPS information, driver's status and so on. The base station also authenticates itself to the nearby cars using its private key, transmits the commitment of the hash chain, and sends all the messages gathered from cars with authentication information.