In this paper it is investigated the roles of key elementary reactions for NO formation in methane-air one-dimensional premixed flame and counterflow diffusion flame, which were studied numerically by using NO kinetics and $C_{2}$ -chemistry complied by Miller and Bowman. The spatial distributions of the reaction rates of 9 main elementary reactions directly related to NO formation and destruction were calculated. Integration of the rates of all reactions in the NO formation across the flame yields the quantitative reaction path diagram, which shows clearly relative importance of each reaction path in NO formation and how it changes with the type and parameters of the flame. The results show that the thermal and Fenimore mechanisms are dominant respectively for learn and rich premixed flames, and the latter is dominant for diffusion flames. In addition, it was found that the HCN recycle route is important for diffusion flame, and that the routes of mutual transformation between NO and NO$^{2}$, and between NO and HNO do not contribute to the net NO formation.