This study considers numerical simulation of the combustion of hydrogen with air, including oxygen and nitrogen, in a burner and the numerical solution of local entropy generation rate due to the high temperature and velocity gradients in the combustion chamber. The effects of equivalence ratio (phi) and oxygen percentage ( c) on the combustion and entropy generation rate are investigated for different phi s (from 0.5 to 1.0) and gamma s (from 10 to 30%). The combustion is simulated for the fuel mass flow rate providing the same heat transfer rate (Q) the combustion chamber in the each case. The numerical calculation of combustion is performed individually for all cases with the help of the Fluent CFD code. Furthermore, a computer program has been developed to calculate numerically the volumetric entropy generation rate distributions and the other thermodynamic parameters by using the results of the calculations performed with the FLUENT code. The calculations bring out that the increase of phi (or the decrease of lambda) reduces significantly the reaction rate levels. The average temperatures in the combustion chamber increase about 70 and 23% with the increases of gamma (from 10 to 30%) and phi (from 0.5 to 1.0), respectively. With the increase of gamma from 10 to 30%, the volumetric local entropy generation rates decrease about 9 and 4% in the cases of phi =0.5 and 1.0, respectively, and while the total entropy generation rates decrease exponentially, the merit numbers increase. The useful energy transfer rate to irreversibility rate therefore improves as the oxygen percentage increases.