A direct numerical simulation (DNS) was applied to nonpremixed counter-flow diffusion flames between oxidizer and fuel ducts. The objective of this study is to evaluate the numerical method for simulation of axisymmetric counterflow diffusion flames. Effects of computational domain size and grid size were scrutinized, and then the method was applied to air-methane diffusion flames. The results at zero gravity conditions were in good agreement with those obtained by the one-dimension flame code OPPDIF. It was confirmed thai the numerical method is applicable to the diffusion flames at the normal gravity conditions since the results clearly showed the effects of buoyancy and velocity ratio.