This study considers numerical simulation of the combustion of methane with air, including oxygen and nitrogen, in a burner and the numerical solution of local entropy generation rate due to high temperature and velocity gradients in the combustion chamber. The effects of equivalence ratio (phi) and oxygen percentage (gamma) on combustion and entropy generation rates are investigated for different 0 (from 0.5 to 1.0) and gamma values (from 10 to 30%). Combustion is simulated for the fuel mass flow rate resulting in the same heat transfer rate (Q)over dot to the combustion chamber in each case. Numerical calculation of combustion is performed individually for All cases with the use of the Fluent CFD code. Furthermore, a computer program has been developed to calculate the volumetric entropy generation rate and the other thermodynamic parameters numerically by using the results of the calculations performed with the FLUENT code. The predictions. show that the increase of phi (or the decrease of lambda) significantly reduces the reaction rate levels. Average temperature in the combustion chamber increases by about 70 and 35% with increase of gamma (from 10 to 30%) and phi (from 0.5 to 1.0) respectively. With increase of gamma from 10 to 30%, volumetric local entropy generation rate decreases by about 9 and 4% for phi = 0.5 and 1.0 respectively, while total entropy generation rate decreases exponentially and the merit numbers increase. The ratio of the rates useful energy transfer to irreversibility therefore improves as the oxygen percentage increases.