The present study is numerically investigated the flame structure of non-premixed counterflow jet flames using the laminar flamelet model Detailed flame structures with the fuel composition of 40% CO, 30% $H_2$. 30% $N_2$ and an oxidizer composition of 79% $N_2$ and 21% $O_2$ in a non-premixed counterflow flame are studied numerically. This study is aimed to investigate the effects of axial velocity gradient and combustion atmosphere pressure on flame structure. The results show that the role of axial velocity gradient on combustion processes is globally opposite to that of combustion atmosphere pressure. That is, chemical nonequilibrium effects become dominant with increasing axial velocity gradient, but are suppressed with increasing ambient pressure. Also, the flame strength is globally weakened by the increase of axial velocity gradient but is augmented by the increase of ambient pressure. However, flame extinction is described better on the basis of only chemical reaction and in this study axial velocity gradient and ambient pressure play a similar role conceptually such that the increase of axial velocity gradient and ambient pressure cause flame not to be extinguished and extend the extinction limit, respectively. Consequently it is suggested that a combustion process like flame extinction is mainly influenced by the competition between the radical formation reaction and the third-body recombination reaction.