Abstract: A nonlinear feedback controller is designed for spacecrafts' attitude control systems based on quaternion. A feedback control law with angular velocity measurement is firstly obtained which guarantees the globally asymptotical stability of the closed-loop systems and the stability of the two desired equilibriums. Then, using a filter of the quaternion to replace the angular velocity measurement, a feedback control law without angular velocity measurement is obtained which can also guarantee the globally asymptotical stability of the closed-loop systems and two stable desired equilibriums. It is important to note that two stable equilibriums can make any solution converge to the equilibrium close to the initial attitude. Finally, a numerical simulation is given to show the advantages of the obtained feedback control laws.