Failure recovery in Internet of Vehicles (IoVs) is critical to high quality service provisioning. The main challenge is how to achieve fast rerouting without introducing high complexity and resource usage due to the dynamic topology and the constraints on bandwidth. In this paper, we propose a traffic prediction-based fast reroute algorithm for use among the vehicles in IoVs. The proposed algorithm uses the Wavelet Neural Network (WNN) model to predict a vehicle's network traffic. When the predicted value is greater than the predefined network traffic threshold, both Adaptive Retransmission Trigger (ART) that contributes to switch to a better alternate path in advance and trigger efficient retransmission behaviors are enabled successively. Performance comparison of our proposed algorithm with Ant-based Delay-Sensitive Vehicular Routing (AntVehiNet) shows that WNNPFR can: (a) maximize the service data delivery rate by load balancing, (b) provide high quality of service delivery for multimedia streams by switching to a better path towards a target node in advance, (c) reduce useless data retransmissions when various network failures occur, and (d) maintain lower routing overhead.