Aiming at the nonlinearunderactuatedstrong coupling and multivariable control problems in trajectory tracking control of quadrotor UAVa cascade global fast Terminal Sliding Mode Control (TSMC) strategy based on Extended State Observer (ESO) is proposed.The control strategy enables the system to perceive promptly and eliminate internal and external disturbances in real timeand guarantees that the system will converge to the state of equilibrium in a limited time.In additionthe stability of the control system is proved by the Lyapunov theorem.The simulation results demonstrate that the proposed control algorithm can improve the robustness of the system and ensure the trajectory tracking accuracy of the quadrotor UAV under the conditions that the dynamic characteristics of the motor and external disturbances are taken into account,and the assumption of small disturbance of attitude angles is avoided.