Vehicular ad hoc network (VANET) provides short range communication for vehicles, achieving information sharing to improve road safety and traffic efficiency. However, public communication between vehicles has led to issues with vehicle communication security and privacy leakage, which seriously restricts the development of VANET. The authentication mechanism can verify the reliability of messages and the validity of identities, thereby ensuring communication security between vehicles. Therefore, this paper proposes a certificateless authentication scheme based on the characteristics of blockchain, such as decentralization, traceability, and tamper resistance, combined with a pairing-free certificateless password mechanism. Through security proofs and analysis, it is demonstrated that we achieve high security and satisfies security requirements such as integrity, traceability, anonymity, and revocability. Furthermore, simulation comparisons with existing schemes show that we have lower computational overhead and communication costs.