The control of nitrogen oxides ($NO_x$) has been a major issue in designing combustion systems, since $NO_x$ play a key role in ozone depletion and the generation of photochemical smog. The characteristics of $NO_x$ emission can be essential information for the development of a clean combustor having suitable reduction methodologies. In the present study, $NO_x$ emission characteristics were evaluated numerically, accounting for the effect of equivalence ratio, stretch rate, pressure, and initial temperature. In general, peak $NO_x$ emission appeared near the equivalence ratio of unity case, and $NO_x$ emission increased with pressure and initial temperature due to the temperature sensitivity in $NO_x$ mechanism. $NO_x$ decreased with stretch rate due to the decrease in residence time in high temperature region. Furthermore, the thermal and prompt mechanisms were evaluated with equivalence ratio for two calculation methods. The conventional methods ignore the interaction of coupled mechanism of thermal and prompt $NO_x$. The reaction path diagram was introduced to understand effective reaction pathways in various conditions.