Considering that the off-line computation of explicit model predictive control for complex fast multi-dimensional constrained systems has the shortages of large amount of computationslow processing speed and high memory usage, we proposed an efficient explicit model predictive control algorithm based on separating saturated region. By combining polyhedron, piecewise affine related concepts and Polya theorem and using the feedback saturation characteristic of explicit controllers, the saturated region was removed and the unsaturated critical region was retained, so as to reduce the number of state partitions and computational complexity. Then, based on the state space simplified model of two subsystems of the decoupled quad-rotor aircraft, we realized rapid and accurate adjustment of attitude angles. The effectiveness and superiority of the proposed algorithm in attitude control of the quad-rotor aircraft have been verified by numerical simulation and hardware-in-the-loop simulation experiments.