Node authentication, non-repudiation and anonymous communication are key roles to provide security in Vehicular Ad Hoc Networks (VANETs). On the other hand, the trade-off between authentication/non-repudiation and anonymous communication may lead to a harmful type of network attack called sybil attack. In such an attack, a malicious node behaves as if it is a large number of nodes. In this paper, we propose an anonymous authentication and sybil attack detection protocol for VANETs called ASAP-V. Experimental results suggest that ASAP-V is more robust against sybil attacks, with lower average detection time than the state-of-art works, also without false-positive and false-negative detections.