A quadratic mapping method based on curvature for mesh generation is presented in this paper. The method starts from the triangulation of 2D parametric surface by applying the Advancing Front Technique (AFT) and Delaunay Triangulation (DT) together with 3D feature information. Then 3D surface mapping from 2D elements is realized by quadratic mapping method with curvature measure information. After that, triangular mesh over 3D surface is automatically generated. Besides, graded mesh control strategy is discussed in the paper for the sake of generating mesh with higher quality. Finally, several application examples are given to show the characteristics of the presented method.