To improve the trajectory tracking accuracy of coaxial multi-rotor UAV under airflow disturbance and rotor fault, a fast terminal sliding-mode fault-tolerant control method is proposed. The fault model of a coaxial 12-rotor UAV was established. A fast terminal sliding-mode control law with a motion loop was designed to convert the trajectory command into the velocity command, and the air flow disturbance and rotor fault were estimated by using the slidingmode adaptive law and the sliding-mode observer respectively. A fast terminal sliding-mode fault-tolerant control law was designed for the speed loop to achieve high precision of the coaxial 12-rotor UAV trajectory tracking. The simulation results show that the proposed method can compensate for the rotor fault and airflow disturbance more effectively, compared with the integrated sliding-mode fault-tolerant control method, and the maximum trajectory tracking error is only 0.3 m, which can accurately estimate the rotor fault within 0.2 s, and the maximum air disturbance estimation error is only 0.2 m/s², which has great trajectory tracking effect.