The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.
 M. Bergdorf, Ivo F. Sbalzarini, and P. Koumoutsakos, “A Lagrangian particle method for reaction–diffusion systems on deforming surfaces”, J. Math. Biol., vol. 61, 2010, pp. 649–663.
 S.-G. Chen, M.-H. Chi, and J.-Y. Wu, “High-Order Algorithms for Laplace–Beltrami Operators and Geometric Invariants over Curved Surfaces”, vol 65, 2015, pp.839-865.
 S.-G. Chen and J.-Y. Wu, "Estimating normal vectors and curvatures by centroid weights", Comput. Aided Geom. Design, vol. 21, 2004, pp. 447–458.
 M. DoCarmo, “Differential geometry of curves and surfaces, Prentice-Hall, Lodon, 1976.
 M. DoCarmo, “Riemannian geometry”, Birkhauser, Boston, 1992.
 E. J. Fuselier and G. B. Wright, “A high-order kernel method for diffusion and reaction-diffusion equations on surfaces”, J. Sci. Comput., vol. 56, issue 3, 2013, pp. 535-565.
 C. Landsberg and A. Voigt, “A multigrid finite element method for reaction-diffusion systems on surfaces”, Comput Visual Sci, vol. 13, 2010, pp. 177–185.
 A. Madzvamuse, A. J. Wathen, and P. K. Maini, "A moving grid finite element method applied to a model biological pattern generator", J. Comput. Phys. vol. 190, no. 2, 2003, pp. 478–500.
 DW Thompson, “On growth and form”, 2nd end, Cambridge University Press, 1942.
 N. Tuncera, A. Madzvamuseb, and A. J. Meir, “Projected finite elements for reaction–diffusion systems on stationary closed surfaces”, Applied Numerical Mathematics, vol. 96, 2015, pp. 45–71.