This work presents a novel control strategy for the trajectory tracking control of the quadrotor unmanned aerial vehicle (UAV) with parameter uncertainties and external unknown disturbances. As a stepping stone, two fixed-time extended state observers (ESOs) are proposed to estimate the external disturbances and/or the parameter uncertainties for the position and attitude subsystems, respectively. Then, the fast terminal sliding mode-based improved dynamic surface control (DSC) approaches are developed. To eliminate the problem of “explosion of complexity” inherent in backstepping method-based controllers, the finite-time command filters and an error compensation signals are used in the design of the dynamic surface controllers. Subsequently, the practically finite-time stability of the closed-loop tracking system is guaranteed by utilizing the proposed control scheme. The simulation results are obtained to demonstrate the effectiveness and fine performance of the proposed trajectory tracking control approaches.