A method considering global performance and local constraints is proposed for constraint attitude control problem. The pseudo-spectral method, with few nodes for lower computation burden, is used as global path planner to obtain attitude path nodes with good global performance. The local controller to track path nodes is advanced by using predictive control method, and the convex constraint formulation with conservation is designed through the analysis of property of geometric constraint and quaternion propagation in linearized dynamics. Simulation results show the effectiveness and feasibility of the method.