This paper deals with the stabilization problem of an underactuated quadrotor UAV system in presence of actuator and sensor faults. The dynamical model of quadrotor while taking into account various physical phenomena, which can influence the dynamics of a flying structure is presented. Subsequently, a new control strategy based on backstepping approach, taking into account the actuator and sensor faults is developed. Lyapunov based stability analysis shows that the proposed control strategy design keeps the stability of the closed loop dynamics of quadrotor UAV even after the presence of these faults. Simulations of the controlled system, illustrate that the proposed control strategy is able to maintain performance levels and to preserve stability under the occurrence of actuator and sensor faults.