A fractional-order, Super-Twisting sliding mode controller is proposed for the trajectory tracking of quadrotor UAVs under external disturbance.Firstly, based on the double closed-loop control strategy, the quadrotor UAV system is decoupled as a position subsystem and an attitude subsystem.Secondly, the sliding mode controller is designed by using the Super-Twisting algorithm, which can realize global finite-time convergence and eliminate system chattering.In order to further improve the control precision and anti-interference performance of the system, a fractional-order differential and integral operator is introduced.Finally, a simulation is conducted in comparison with the Super-Twisting sliding mode and the integral terminal sliding mode, and the superiority of the proposed algorithm is verified.