An L₁ adaptive block backstepping attitude controller is proposed for the attitude control problem of a quadrotor UAV. The attitude kinematical model of quadrotor is translated into a class of multi-input multi-output uncertain nonlinear system. According to the strict feedback architecture of the system, the block backstepping controller is designed for the out-loop subsystem. In order to compensate the influence of the existing uncertainties of exterior disturbances and interior parameters perturbation in the inner-loop subsystem, the L₁ adaptive control algorithm is introduced. The stability analysis shows that the closed-loop system signals are uniformly bounded. The simulation and attitude stabilization experiments show the effectiveness and robustness of the proposed control architecture.