Flying ad hoc networks (FANETs), which are composed of autonomous flying vehicles, constitute an important supplement to satellite networks and terrestrial networks, and they are indispensable for many scenarios including emergency communication. Unfortunately, the routing therein is largely affected by rapid topology changes, frequent disconnection of links, and a high vehicle mobility. In this paper, an intelligent routing strategy based on deep reinforcement learning (DRL) is proposed, which is decentralized and takes into account the status of symmetrical nodes in two hops. In order to perceive the local dynamics of the network as comprehensively as possible, the location, moving speed, load degree, and link quality of the nodes are considered into the setting process of state elements in the method. The nodes can select the neighboring node adaptively according to the Q values calculated by the model obtained through the training of Deep Q-Networks. The simulation and analysis show that the proposed method possesses good convergence characteristics and has obviously better performance compared with several common methods.