The asymptotic structure of unstrained, laminar, fuel-rich, premixed methane flame is analyzed by using a reduced chemical-kinetic mechanism made up of three global steps. Analysis is carried out for values of equivalence ratio greater than 1.3. The flame structure is presumed to comprise three zones: an inert preheat zone, a thin reaction zone, and a post-flame zone. In contrast to previous asymptotic analyses of lean flames and moderately rich flames, where the reaction zone of these flames was presumed to be made up of two layers, for rich flames analyzed here all chemical reaction are presumed to take place in one layer, The structure of the reaction zone of rich flames is obtained by integrating two second order ordinary differential equations, one giving the consumption of fuel and the other the consumption of oxygen. For values of equivalence ratio greater than 1.3, burning velocities obtained from the asymptotic analysis are found to agree reasonably well with those obtained using a chemical-kinetic mechanism made up of elementary reactions.