A parameterized Free-Form Deformation (FFD) method with mapping design parameters for aerodynamic shape optimization of turbine is developed. According to the expanded feature of aerodynamic analysis grid in the spanwise direction, 3D control volume for mesh deformation of aerodynamic analysis grid is decomposed into a number of 2D control planes at different blade heights. The 2D control plane is designed by analogy with the topology structure of the aerodynamic analysis grid on the 2D cross section, which is consisted of blade profile control points and flow passage control points. The blade profile control points are created by the design parameters to achieve the parameterized mesh deformation. The movement of flow passage control points follows the movement of blade profile control point in order to improve grid quality. The mesh deformation results show that the developed method can morph aerodynamic analysis grid with mapping design parameters and the quality of deformed grid is almost as the same as the original. Subsequently, aerodynamic shape optimization of a single turbine stage is implemented based on the parameterized mesh deformation method proposed in this work. Optimization results show that the developed method can effectively improve turbine performance and provide support for turbine design. (C) 2018 Elsevier Ltd. All rights reserved.