The objective of my thesis work is to model laminar diffusion flame using simple chemical reacting system (SCRS) combustion model. This combustion model assumes that the chemical reactions are infinitely fast and take place via a global one-step without intermediate reactions. The detailed kinetics is considered unimportant as this model is concerned with the global nature of the combustion process and with the final major species concentration. The model is developed using C++ computer language. The algorithm used for solving Navier-stokes and mixture fraction equations is the fractional step method for compressible flow with low Mach number. Low Mach number approximation is used in simplifying the flow equations as flow speed is very low compared to speed of sound. By modelling diffusion flame through an SCRS, flame temperature and species concentration are retrieved from mixture fraction field. The thesis is divided into six chapters. Chapter 1 is an introductory chapter about objective, scope and justification of the work. In Chapter 2 the conservation laws of fluid motion are explained. In chapter 3, the discretization of the computational domain and discretization of different terms in the transport equations are explained. The fractional step method algorithm for incompressible flow and compressible flow with low Mach number are illustrated in chapter 4.In chapter 5, the code is verified for incompressible flow by the method of manufactured solution (MMS) and by comparing code results with benchmark solutions of driven cavity and differentially heated cavity for incompressible flow, while for compressible flow code result is compared with benchmark solution of differentially heated cavity with high temperature difference. In chapter 6 SCRS model is discussed and the simulation results for diluted methane diffusion flame are presented. The simulation results for the laminar diffusion flame show that the flame reaches its maximum temperature at the stoichiometric mixture fraction contour line where oxygen and fuel are completely consumed. The flame length is changed by altering fuel or oxidant streams velocities. Also changing the percentage of nitrogen gas in the fuel and oxidant stream affect both flame length and flame maximum temperature.