This paper proposes an auto-tuning adaptive proportional-integral-derivative control (APIDC) system for attitude and position stabilization of quadrotor unmanned aerial vehicle (UAV) under parameter uncertainties and external disturbances. By employing sliding mode control as the adaptive mechanism, this technique can overcome the manual controller's re-tuning gains in a proportional-integral-derivative controller. Furthermore, a fuzzy compensator is used to eliminate the chattering phenomena caused by the sliding mode control. The auto-tuning process is based on the gradient descent technique and the Lyapunov stability theorem. Using simulations, the proposed APIDC scheme is able to achieve a satisfactory attitude and position tracking performance of the quadrotor UAV. The proposed APIDC system also shows high robustness under parameter uncertainties and external disturbances.