Research on reducing the NO emission from internal combustion engine is a challenging work. NO emission prediction model plays a significant role in simulation-based research. According to extended Zeldovich, the determination of equilibrium concentration of combustion products is vital in the prediction of NO formation. Besides the well known STANJAN and Newton-Raphson iteration, Trust-region dogleg, PSO (Particle Swarm Optimization), and GA (Genetic Algorithm) are added to investigate the performance of those methods on the determination of combustion products. Twelve species are considered in the combustion products. STANJAN uses minimizing Gibbs energy to derive the needed nonlinear equations while the others use Equilibrium Constant Method. In terms of the results, it is found that Trust-region dogleg method shows the best performance which achieves the desired accuracy within 0.1 s and the calculated results are comparable to STANJAN. In addition, perturbed PSO also reveals excellent global convergence capability. On the contrary, unmodified Newton-Raphson is unsuitable for this problem and Newton-Raphson downhill shows satisfactory performance neither. According to the results of parameter study, the equilibrium concentrations of combustion products are greatly influenced by equivalence fuel-air ratio and temperature but little affected by pressure. The NO formation process shows good agreement with AVL BOOST. Compared to measured value, the best-predicted emission value reaches -5.45% but the worst drops to -17.72%.