Abstract: In order to reveal the influence of different factors of effective radius of gas extraction from coal seam borehole, predict the effective radius of coal seam gas extraction more accurately and improve the gas extraction rate, this paper built a mathematical model of gas extraction based on the theories of gas migration, seepage and Klinkenberg effect in coal seam; COMSOL software was used to simulate the influence of five factors on the effective radius of coal seam gas extraction, including initial gas pressure, permeability, negative pressure of extraction, aperture and extraction cycle. The results show that the effective radius of coal seam gas extraction is negatively correlated with the change of initial gas pressure, and positively correlated with the change of permeability, negative pressure, borehole diameter and extraction cycle. The grey relational mathematical model is used to analyze the five influencing factors in primary and secondary order according to the numerical simulation results, it is found that the initial gas pressure has the strongest influence on the effective radius of gas extraction, followed by the permeability, and the negative pressure of gas extraction has the weakest influence. The research results can provide theoretical basis for underground construction of coal seam gas extraction technology.