One of the important characteristics of vehicular ad hoc networks is the high mobility of nodes. It is significant to select stable links for transmitting data in routing protocols to solve the problem of frequent link breakage caused by free movement of nodes. To solve this problem, we propose an improved ondemand distance vector routing protocol (AODV) scheme with link stability, namely GFAODV (AODV with GASAFNN). The algorithm uses fuzzy neural networks to calculate the node information in the initialization and selection stages to get node stability. Then we evaluate the link quality, and select the stable link which has fewest hops based on link stability and hop count. In the routing maintenance phase, the parameters of the fuzzy neural network are optimized in real time according to the actual environment by using the genetic simulated annealing algorithm, which guarantees the consistency between calculated node stability and the actual situation. Experiments show that the GFAODV routing protocol outperforms the AODV in terms of average delay, packet delivery rate and routing overhead.