With the aim to solve the problem of shape distortion when generating the finite element mesh of parametric surfaces, mapping method was used. But mapping method could generate distortion elements which lead to poor quality meshes easily. Based on the Riemannian metric, a combined advancing front technique (AFT) and Delaunay triangulation（DT） method were applied. In this algorithm, Riemannian metric was considered, and background grids of parametric space were generated by improved AFT. When background grids of parametric space were refined to counteract mapping distortion, the traditional Delaunay incremental insertion kernel was replaced by inserting the center of triangle circumscribed ellipse, and the algorithm for locating ellipse center and judging whether nodes within ellipse. The mapping distortion and algorithm efficiency were considered by the algorithm by introducing Riemannian metric and reasonable background mesh. Examples show that the new method is easy to implement. The mesh which has good stability and high quality can be generated.