The quadrotor unmanned tracking control problem in the external disturbance and constraints of the output error is investigated in this paper. Firstly, the dynamics model of the quadrotor UAV is transformed into a strict feedback form with the external disturbances. Then, the backstepping method is used to design the controller, the barrier Lyapunov function is introduced to ensure the prescribed performance of the tracking error, the disturbance observer is designed to estimate the external disturbance, and the derivatives of some virtual control inputs in the attitude subsystem are estimated through the filter. The stability analysis shows that the designed controller can guarantee the bounded stability of the tracking error, and the tracking error remains within the preset boundary. Finally, the simulation results verify the effectiveness of the proposed control strategy.