Vehicular ad hoc network (VANETs) improves road safety and efficiency by organizing vehicles and infrastructure to provide a platform for application deployment. The availability of vehicles and infrastructure is critical to the operation of applications. Accurate failure detector (FD) has been one of the fundamental components for maintaining high availability in VANETs. However, it is hard to find the vehicle failure accurately and timely due to the dynamic nature of VANETs caused by the high mobility of vehicles and communications link failures. Therefore, it is important to achieve an accurate FD which can cope with the high mobility of VANETs. In this paper, we propose a dead reckoning based FD, called DR-FD. It can predict the mobility of vehicle accurately and avoid the impact of link failures on the detection results by the cooperation between vehicles. Experimental results are provided to confirm that the proposed DR-FD method can achieve at most 20% reduction in detection time, 30% improvement in mistake rate and 20% improvement in overhead.