In this paper, a robust integral sliding mode controller is designed for the position and attitude control of an autonomous quadrotor with under-actuated characteristics. The designed controller can stabilize the pitch angle and roll angle while the three position and yaw angle could converge to the desired values. Furthermore, the flight controllers are derived via the Lyapunov theory, which can guarantee that all the system state trajectories reach and maintain on the sliding surfaces. The advantage of the integral sliding mode control is that it is insensitive to the modelling errors, parameter uncertainties and other disturbances, and it can improve the steady-state response of the system as well. The chattering of the controller is reduced by a designed boundary layer. The performance of the proposed controllers is compared with the PD controller with the simulation experiments, which can achieve better robustness and tracking capability.