A method for analyzing influencing factors of complex systems based on multi-dimensional Gaussian Bayesian classification algorithm is proposed, classification models for diverse range of PM_2.5 are established, and then the analysis of the key influencing factors on complex systems is carried out in combination with Mahalanobis distance. Based on the weather and air quality data of Hefei City from 2013 to 2018, 8 main influencing factors for PM_2.5, such as PM₁₀, SO₂, NO₂, CO, O₃ and so on, are screened out, and then the correlation between PM_2.5 and the influencing factors is analyzed using scatter matrix. The PM_2.5 analysis model based on Gaussian Bayesian classifier is established with these data. It is found that PM_2.5 has a strong positive correlation with CO concentration, is selective to NO₂, and has a negative correlation with O₃. As for CO and SO₂, a certain competitive mechanism between the two factors in the production of PM_2.5 is observed.