Combustion of gaseous fuel combustor in a high temperature vitiated air stream was studied with computer simulation. It is for application to afterburner of gas turbine engine which the exact mechanism is not yet clarified. As the jet velocity from fuel nozzle is very high and the geometry of combustor is three dimensional complex structure, many time and money are required to have good results. To consider this demerit, it is simplified to 2-dimensional and modified with the nozzle hole area to same area of annual status. As the thickness of annual is too thin, it is to divide with the many grids for reasonable results. Accordingly, new method which injected fuel mass, momentum and energy are added to source terms of each governing conservation equation as a source terms is introduced like as two phase analysis. Reaction rate is determined by taking into account the Arrhenius reaction based on a single step reaction mechanism. It is focused to temperature and product concentration distribution at each equivalence ratio of inlet hot product.