An entropy analysis and design optimization methodology is combined with airfoil shape optimization to demonstrate the impact of entropy generation on aerodynamics designs. In the work herein, the entropy generation rate is presented as an extra design objective along with lift-drag ratio, while the lift coefficient is the constraint. Model equation, which calculates the local entropy generation rate in turbulent flows, is derived by extending the Reynolds-averaging of entropy balance equation. The class-shape function transform (CST) parametric method is used to model the airfoil configuration and combine the radial basis functions (RBFs) based mesh deformation technique with flow solver to compute the quantities such as lift-drag ratio and entropy generation at the design condition. From the multi-objective solutions which represent the best trade-offs between the design objectives, one can select a set of airfoil shapes with a low relative energy cost and with improved aerodynamic performance. It can be concluded that the methodology of entropy generation analysis is an effective tool in the aerodynamic optimization design of airfoil shape with the capability of determining the amount of energy cost.