In this paper, we investigate a class of optimal control problems for turbofan aero-engines considering external disturbances. The alternating direction method of multipliers (ADMM) is embedded in the framework of robust model predictive control (RMPC), which is not only able to reach a predetermined value of the engine fan speed, but is also developed to maintain the robustness of the engine control system. First, to consider the optimal control strategy for the worst-case scenario, this optimal control problem is formulated as a minimum-maximum convex optimization problem with constraints. Second, through a transformation technique, the problem can be equivalently described by a variational inequality, which is then transformed into a quadratic programming (QP) problem using a proximal point algorithm (PPA). Finally, the ADMM algorithm is used to solve a series of optimization subproblems based on the structural characteristics of the model. Computational examples illustrate the solution efficiency and robustness of the improved algorithm (RMPC-ADMM).