In intelligent transportation systems, the cooperation between vehicles and the road side units is essential to bring these systems to fruition. Vehicular ad hoc networks (VANETs) are a promising technology to enable the communications among vehicles on one hand and between vehicles and road side units on the other hand. However, it is a challenging task to develop a reliable routing algorithm for VANETs due to the high mobility and the frequent changes of the network topology. Communication links are highly vulnerable to disconnection in VANETs; hence, the routing reliability of these ever-changing networks needs to be paid special attention. In this paper, we propose a new vehicular reliability model to facilitate the reliable routing in VANETs. The link reliability is defined as the probability that a direct communication link between two vehicles will stay continuously available over a specified time period. Furthermore, the link reliability value is accurately calculated using the location, direction and velocity information of vehicles along the road. We extend the well-known ad hoc on-demand distance vector (AODV) routing protocol to propose our reliable routing protocol AODV-R. Simulation results demonstrate that AODV-R outperforms significantly the AODV routing protocol in terms of better delivery ratio and less link failures while maintaining a reasonable routing control overhead.