In this paper, an adaptive fuzzy command filter backstepping (CFB) asymptotic tracking control method is proposed for trajectory tracking of quadrotor unmanned aerial vehicle (QUAV) with unknown parameters and external disturbance. The asymptotic tracking control method is adopted which can make sure that the tracking errors asymptotically converge to zero. Then, the CFB is used to avoid computational complexity and the error compensation system is added to eliminate the effect of filtering errors. Finally, the Lyapunov function is constructed to prove that the tracking errors can achieve asymptotic tracking. The feasibility of control method has been verified through Matlab simulation.