Vehicular Ad hoc NETwork (VANET) provides traffic safety and efficient traffic management by taking advantage of messages that are quickly interchanged among vehicles and some infrastructures. The integrity and non-repudiation of messages and vehicle privacy in VANET are quite critical. Pseudonym technology is a practical strategy to ensure these three properties. However, the functionalities and performance of previous related works cannot satisfy the requirements of VANET. This paper proposes a secure message-broadcasting method based on Identity-Based Encryption (IBE) in VANET. This work protects driver/vehicle privacy and track. The method also provides authentication, integrity, non-repudiation, confidentiality, forward secrecy, anonymity, untraceability and responsibility to satisfy the security requirements of VANET communication.