Quaternion-based attitude determination system is considered since it can represent all physical attitudes, but not uniquely. An inappropriate quaternion-based control law would imply to a non-efficient control effort and difficulty in guaranteeing global stability. Many research efforts decide to add complexity in the controller by using jump-discontinuity function and/ or hybrid system. In contrast, this paper proposes a continuous quaternion-based attitude control system with an augmented dynamic that guaranteed to be able to regulate any physical state asymptotically. The effectiveness of the designed system is verified through simulations.