This paper develops a nonlinear hierarchical control for quad-rotors to accomplish trajectory tracking manoeuvres. The rotation matrix is applied to represent the attitude of the quad-rotor. The position and attitude loop controls are designed separately. During the position loop control design, an auxiliary system with saturation control project is developed, which can not only ensure a bounded applied thrust, but also preserve the constrained requirement in the command rotation extraction. As an intermediate step, the minimum rotation principle is employed to extract the command rotation matrix. Then, using the property of the rotation matrix, an applied torque with the corresponding initial condition constraint is designed to complete the attitude tracking. Based on the analysis theory of the hierarchical system, it's proven that, with the developed applied thrust and torque, the tracking errors of the quad-rotor system are asymptotically stable. Finally, simulations illustrate the theoretical results.