A self-adaptive center-mutation differential evolution(SCDE) was developed for the high-dimension complex optimization problems,and applied to the high fidelity aerodynamic optimization design of the multi-stage oxidizer turbine blade shapes for cryogenic rocket engines.Performances of design candidates were evaluated by the turbine efficiency based on three-dimensional airfoil geometry design and single-channel flow analysis using commercially available CAD(computer aided design) and CFD(computational fluid dynamics) packages.The reasonable solution is finally achieved,namely,turbine efficiency of the optimal design is 5.25% higher than that of the original one.