The modeling and control for a quadrotor UAV are presented in this paper.The theoretic methods are used to model the UAV,and the models for the motors and the rotors of the vehicle are described in detail.Quaternions are used to present the vehicle's model for attitude control.The Eular angles are first transformed into quaternions,and the error quaternions are calculated.The required angles and axis are derived from quaternions.The velocity controllers based on quaternions in each direction are designed,and compared with PID controllers.The result shows that the control laws based on quaternions are more effective in controlling the UAV at high speed.