Unmanned aerial vehicle (UAV)’s fault-control problem was studied in this paper, and data-driven fault-tolerant control scheme was developed for acceleration tracking control of UAV in order to cope with the uncertainties induced by aerodynamic damage. A linear UAV dynamic model was given with reasonable assumptions, and the acceleration tracking control for UAV was converted to solving an infinite-horizon optimal control problem. The augmented algebraic Riccati equation (ARE) is derived, and its solution stability is proved based on Lyapunov theory. The data-driven control algorithm is further derived for online solving of the augmented ARE with only using flight data. The proposed algorithm is based on experience replay of flight data rather than model knowledge, so it greatly reduces the effect of uncertainties induced by aerodynamic damage on the flight control system for UAVs. Finally, the effectiveness of developed algorithm is verified through the numerical simulations under different uncertainties induced by aerodynamic damage.