Privacy and security should be paid much more attention in secure vehicular ad hoc networks (VANETs). However, as far as we know, few researches on secure VANET protocols have addressed both the privacy issues and authenticated key establishment. Therefore, in this work, a lightweight authenticated key establishment scheme with privacy preservation to secure the communications between mobile vehicles and roadside infrastructure in a VANET is proposed, which is called SECSPP. Our proposed scheme not only accomplishes vehicle-to-vehicle and vehicle-to-roadside infrastructure authentication and key establishment for communication between members, but also integrates blind signature techniques into the scheme in allowing mobile vehicles to anonymously interact with the services of roadside infrastructure. We also show that our scheme is efficient in its implementation on mobile vehicles in comparison with other related proposals.