A new skeletal mechanism, consisting of 16 species and 72 reactions, has been developed for lean methane–air premixed combustion from the GRI-Mech 3.0. The skeletal mechanism is validated for elevated unburnt temperatures (800 K) and pressures up to 4 atm, thereby addressing realistic gas turbine conditions. The skeletal mechanism is obtained by applying the directed relation graph method and performing sensitivity analysis on the detailed mechanism. The mechanism has been validated for flame speed and flame structure in a wide range of conditions and configurations. A good agreement between the skeletal mechanism and GRI-3.0 was obtained. The configurations considered include one-dimension laminar premixed flames, laminar non-premixed counterflow burners, and two- and three-dimensional unsteady configurations with variations of temperature, pressure, and composition. The skeletal mechanism allows for the inclusion of accurate finite rate chemistry in large-scale direct numerical simulations of lean turbulent premixed flames. In a large-scale direct numerical simulation, the use of the skeletal mechanism reduces the memory requirements by more than a factor of 3 and accelerates the simulation by a factor of 7 compared with the detailed mechanism. The skeletal mechanism is suitable for unsteady three-dimensional simulations of methane turbulent premixed, non-premixed, and globally lean partially premixed flames and is available as supplementary material.