Abstract: In order to study the relationship between the gas drainage effect with dilling along coal seam and the drainage radius as well as the drainage time, bas ed on the seepage theory, gas state equation and gas content calculation equation, a mathematical model of the timespace evolution law for the gas drainage in the mi ning seam was established.With the application of Comsol numerical simulation, based on the engineering background of No. 1320-11 coal mining face in Zhongheng Mi ne, the gas pressure distribution within the radial scope of a single borehole under the different drainage time was obtained, a dynamic variation relationship between th e drainage radius and the drainage time was analyzed and the logarithm function relationship of the time-space evolution in the process of the gas drainage was further derived.The comparison experiments of the borehole gas drainage under the condition of different drainage radius were conducted.The function relationship rationality and accuracy on the space and time evolution law of the gas drainage when the drainage radius less than 2 m or the drainage time within 180 days was calculated and verified.The function relationship conforms actual extraction law.