This paper proposes two different adaptive robust sliding mode controllers for attitude, altitude and position control of a quadrotor. Firstly, it proposes a backstepping non-singular terminal sliding mode control with an adaptive algorithm that is applied to the quadrotor for free chattering, finite time convergence and robust aims. In this control scheme instead of regular control input, the derivative of the control input is achieved from a non-singular terminal second-layer sliding surface. An adaptive tuning method is utilized to deal with the external disturbances whose upper bounds are not required to be known in advance in the inner loop. Secondly, a nonlinear disturbance observer based on the integral sliding mode with adaptive gains is proposed for position control, which is known as the outer loop. Stability and robustness of the proposed controller are proved by using the classical Lyapunov criterion. The simulation results demonstrate the validation of the proposed control scheme.