Turbulence affects both combustion and NO formation. Fluctuation correlations are ideally used for quantitative analysis. From the instantaneous chemical reaction rate expression,ignoring the third-order correlation terms, the averaged reaction rate will have four terms, including the term of averaged-variable product, a concentration fluctuation correlation term, and temperature-concentration fluctuation correlation term. If the reaction-rate coefficient is denoted as K, the temperature fluctuation would be included in the K fluctuation. In order to quantitatively study the effect of turbulence on NO formation in methane-air swirling combustion, various turbulencechemistry models are tested. The magnitudes of various correlations and their effects on the time-averaged reaction rate are calculated and analyzed, and the simulation results are compared with the experimental measurement data. The results show that among various correlation moments, the correlation between the reaction-rate coefficient K fluctuation with the concentration fluctuation is most important and is a strong nonlinear term. The instantaneous chemical reaction rate expression, ignoring the third-order correlation terms, the averaged reaction rate will have four terms, including the term of averaged-variable product , a concentration fluctuation correlation term, and temperature-concentration fluctuation correlation term, and temperature-concentration coefficient is denoted as K, the temperature fluctuation would be included in the K fluctuation. In order to quantitatively study the effect of turbulence on NO formation in methane-air swirling combustion, various turbulencechemistry models are tested. The magnitudes of various correlations and their effects on the time-averaged reaction rate are calculated and analyzed, and the simulation results are compared with the experimental measurement data. correlation moments, the correlation between the reaction-rat e coefficient K fluctuation with the concentration fluctuation is most important and is a strong nonlinear term.