The vehicular ad hoc networks (VANETs) face serious privacy threats, due to the numerous vehicles, variable node speeds and network openness. To tackle the threats, this paper proposes a conditional privacy protection (CPP) mechanism based on group signature anonymous authentication and the cryptographic algorithms of bilinear pairings on elliptic curve. Unlike most existing group signature mechanisms, this mechanism can achieve anonymous and nonconnectable conditions at the same time, and allow the trust authority (TA) to track the identity of the sender of any controversial message. Finally, simulation results show that the CPP outperformed the group signature-based (GSB) protocol and the human anonymous keysbased (HAB) protocol in verification speed, tacking efficiency and scalability.