is paper aims at solving the end-to-end delay-constrained routing problem in a local way for flying ad hoc networks (FANETs). Due to the high mobility, it is difficult for each node in FANETs to obtain the global information. To solve this issue, we propose an adaptive delay-constrained routing with the aid of a stochastic model, which allows the senders to deliver the packets with only local information. We represent the problem in a mathematical form, where the effective transmission rate is viewed as the optimization objective and the link quality and end-to-end delay as the constraints. And, some mathematical tools are used to obtain the approximate solutions for the optimization problem. Before designing the routing scheme, the senders calculate the transition probability for its relay node by jointly considering local delay estimation and expected one-hop delay. en, the sender transmits the packets to their relay node with transition probability. Finally, we prove the convergence of the proposed routing algorithm and analyse its performances. e simulation results show that the proposed routing policy can improve the network performance effectively in terms of throughput, loss rate, and end-to-end delay.