Unmanned aircraft systems can perform some more dangerous and difficult missions which manned aircraft systems cannot perform. For tasks with high complexity, such as air combat, maneuvering decision mechanism is required to sense the combat environment and make the optimal strategy in real time. This paper formulates one-to-one air combat maneuvering problem in 3D environment, and proposes an approximate dynamic programming approach to make optimal maneuvering decisions automatically. The aircraft searches for combat strategies based-on Reinforcement Leaning, while sensing the environment, taking available maneuvering actions and receiving feedback reward signals. To solve the problem of dimensional explosion in the air combat, the proposed method is implemented through feature selection, trajectory sampling, function approximation and Bellman backup operation in the air combat simulation environment. This approximate dynamic programming approach provides a fast response to rapid changing tactical situations, and learns effective strategies to fight against the opponent aircraft.