Nowadays, Vehicular Ad hoc Networks (VANETs) are popularly known as they can reduce traffic and road accidents. These networks need several security requirements, such as anonymity, data authentication, confidentiality, traceability and cancellation of offending users, unlinkability, integrity, undeniability and access control. Authentication is one of the most important security requirements in these networks. So many authentication schemes have been proposed up to now. One of the well-known techniques to provide users authentication in these networks is the authentication based on the smartcard (ASC). In this paper, we propose an ASC scheme that not only provides necessary security requirements such as anonymity, traceability and unlinkability in the VANETs but also is more efficient than the other schemes in the literatures.