Vehicular Ad hoc Networks (VANETs), whose main objective is to provide road safety and enhance the driving conditions, are exposed to several kinds of attacks such as Denial of Service (DoS) attacks which affect the availability of the underlying services for legitimate users. We focus especially on the greedy behavior which has been extensively addressed in the literature for Wireless LAN (WLAN) and for Mobile Ad hoc Networks (MANETs). However, this attack has been much less studied in the context of VANETs. This is mainly because the detection of a greedy behavior is much more difficult for high mobility networks such as VANETs. In this paper, we propose a new detection approach called GDVAN (Greedy Detection for VANETs) for greedy behavior attacks in VANETs. The process to conduct the proposed method mainly consists of two phases, which are namely the suspicion phase and the decision phase. The suspicion phase is based on linear regression mathematical concept while decision phase is based on a fuzzy logic decision scheme. The proposed algorithm not only detects the existence of a greedy behavior but also establishes a list of the potentially compromised nodes using three newly defined metrics. In addition to being passive, one of the major advantages of our technique is that it can be executed by any node of the network and does not require any modification of the IEEE 802.11p standard. Moreover, the practical effectiveness and efficiency of the proposed approach are corroborated through simulations and experiments.