A finite element method to reconstruct 3D surface from the scattered data is presented in the paper. Based on the theories of optimal approximation and data smoothing, a positive definite functional is constructed and minimized by using the finite element best-fitting technique, then the optimal solution is obtained and the 3D surface is reconstruct by eight-node isoparametric finite element interpolation. The influence of noise in input data is eliminated effectively by the smoothing-finite element method. The number of input data required in the presented method is less than that in finite element fitting. The surface reconstructed is of high approximating precision and good smoothness. Numerical results show that this method is simple and expedient to use.