The objective of this paper is modeling the mechanism of high pressure and high temperature catalytic oxidation of natural gas, or methane. The model is two-dimensional steady-state, and includes axial and radial convection and diffusion of mass, momentum and energy, as well as homogeneous (gas phase) and heterogeneous (gas surface) single step irreversible chemical reactions within a catalyst channel. Experimental investigations were also made of natural gas, or methane combustion in the presence of Mn-substituted hexaaluminate catalysts. Axial profiles of catalyst wall temperature, and gas temperature and gas composition for a range of gas turbine combustor operating conditions have been obtained for comparison with and development of a computer model of catalytic combustion. Numerical calculation results for atmospheric pressure agree well with experimental data. The calculations have been extended for high pressure (10 atm) operating conditions of gas turbine.