This study investigated a numerical prediction procedure for a coaxial turbulent diffusion flame with swirl in an axisymmetric combustion chamber. The main parameters taken into consideration were the effect of the degree of swirl imparted to the annular air jet and the air and fuel mass flow rates. A two-equation turbulence model was embodied combustion with clipped Gaussian probability distribution function for the mixture fraction variable. As the air flow rate and the degree of swirl increase, the flame length decreases. Furthermore the local probability distribution function has been obtained according to the local flow variables.