This paper presents a distributed formation tracking control strategy which acts on multiple quadrotor unmanned aerial vehicles (QUAVs) formation control under external disturbance and asymmetric output error constraints. An asymmetric barrier Lyapunov function (BLF) is applied to ensure the constraint of output error. Based on graph theory and backstepping control method, a distributed formation controller is designed to achieve the formation and maintenance of formations, where external disturbance is handled by disturbance observer (DO). In the framework of Lyapunov theory, the bounded stability of the closed-loop system is proved, and the output error is remained within the constraint range. The superiority and effectiveness of the designed control strategy is verified by the compared simulation.