The newly developed generalized function of airfoil profiles of wind turbine based on Trajkovski conformal transform theory can be used to fit the existing airfoil profiles and create the new ones by adjusting the coefficients of the generalized function. In this approach, the geometrical scale factor a, which was taken as a constant 0.25, has a significant impact on the curvature smooth continuity which will affect the aerodynamic performances of the airfoil. In this paper, the functional integral theory of wind turbine airfoils is studied. Furthermore, the advantage and the importance of curvature issue for airfoil surface are discussed in detail. It is found that, when different existing airfoils were analyzed using the generalized function, the geometrical scale factor a reaches an unexpected lower value. Based on curvature smooth continuity theory, a new method is presented to correct the geometrical scale factor a. As a result, the curvature smooth continuity of the fitting profile has been greatly improved, compared with that of the original profile. As an application of this new method, the DU93-W-210 airfoil is improved with the corrected geometrical scale factor a, and optimized using genetic algorithm (GA) method by controlling the coefficients of the shape function, leading to a new airfoil. Comparatively, the aerodynamic performances of the new airfoil such as maximum lift coefficient, maximum lift-drag ratio, roughness insensitivity and so forth are better than the DU93-W-210 airfoil performances. The achieved results show that this novel method is feasible to optimize airfoils of wind turbine. (C) 2012 Elsevier Ltd. All rights reserved.