In Vehicle-to-Vehicle (V2V) communication networks, vehicles broadcast their safety-critical information to alert nearby vehicles of possible collisions. It is necessary to provide secure wireless communications for V2V safety applications to prevent unauthorised entities from tampering with the broadcast data. A Certificate Authority (CA) can provide trust and secure communications among drivers in V2V networks. However, the disclosure of drivers' unique public keys from their certificates will allow unauthorised entities to trace drivers' movements and locations they visit. Revealing such information without consent from drivers is a violation of their privacy. In this paper, we propose a broadcast protocol for V2V safety applications that provides anonymity for drivers. In our scheme, drivers frequently change their public keys using the digital signature algorithm. The CA is not required to authenticate the generated public keys. The recipients of a signed message can verify the correctness of the signature without identifying the signer.