Towards the attitude control of quadrotor aircraft with model uncertainties and unknown external disturbances, this paper proposed a fast-continuous nonsingular terminal sliding mode control strategy based on nonlinear disturbance observer. In this controller, a nonlinear disturbance observer was used to estimate and compensate the disturbances, which improved the stability of the system. In view of the finite time convergence characteristics, the non-singular terminal sliding mode surface was adopted to design the control law so that it improved the convergence rate of the controller. The Lyapunov function was applied to prove the stability of the controller. Then, the flight dynamics of quadrotor were analyzed and the dynamical model was established. Meanwhile, an artificial bee colony algorithm was introduced to optimize the parameters in the controller and to enhance the control performance. Finally, two numerical simulation cases were conducted to demonstrate the effectiveness of the proposed controller. All the results had shown that compared with other control algorithms, the proposed control algorithm was superior to others in terms of convergence speed, tracking accuracy and disturbances estimation ability, which had an engineering application value.