The dynamics of a quadrotor has the characteristics of underactuation, strong coupling, and nonlinearities, which makes the controller design difficult. Aimed at stabilizing the attitude of a quadrotor, In this paper, we establish the dynamics of the quadrotor. Based on the simplified dynamics model, we design a backstepping sliding based controller using Barrier Lyapunov Functions. Numerical examples and comparisons with traditional backstepping approach are provided to show the effectiveness and the superiority of the proposed control strategy.