In this work, a robust trajectory tracking control strategy is developed for the quadrotor unmanned aerial vehicle (QUAV) with unknown external disturbance. The nonlinear dynamic model of QUAV is established. Different from the traditional disturbance observer and adaptive estimation method, this paper adopts the interval observer technique to approximate the upper and lower bounds of the unknown disturbance. In this way, the proposed interval observer can cover its all possible values and show its scope in real time, especially before the disturbance error estimation converges. Combining with the backstepping approach, a robust tracking control approach is proposed to ensure that the desired trajectory can be successfully followed. Finally, comparative numerical simulation results are provided to evaluate the presented robust tracking controller.