A design of controller for a quadrotor vehicle with one rotor failure is proposed based on back-stepping approach, to ensure the safety of vehicle when ordinary controllers are ineffective under one rotor failure. According to the rotational and translational motion equations of the quadrotor with one rotor failure, the controller is divided into inner and outer ring. An attitude control loop is adopted to perform the attitude tracking control, and a position loop is proposed to control the position of the vehicle. Although the controller sacrifices the controllability of the yaw state, the vehicle can reach position tracking, and achieve the near-hover flight state in which roll and pitch angles are zero and the angular speed around the vertical axis is a nonzero constant. The simulation results demonstrate the effectiveness of the proposed controller. The results show that the absence of controllability of the yaw state of the quadrotor vehicle will not threaten the aircraft security or its trajectory tracking. The study confirms that a quadrotor vehicle with a rotor failure is still controllable.