Abstract: In order to study the permeability of deep coal seam with time-dependent effect during the long-term extrac- tion process,the improved porosity and permeability model coupling with gas desorption effect and time-dependent effect was developed by incorporating mean effective stress into the gas migration equation. By using COMSOL Mul- tiphysics,the process of gas migration around the borehole was calculated quantitatively. In combination with the field data,the variation law of gas seepage field with or without time-dependent effect was compared and analyzed,and the law of gas migration in deep coal seam during long-term extraction was simulated and analyzed. The results show that coal seam permeability increases exponentially with gas pressure decreasing. The porosity and permeability simulation results considering time-dependent effect are significantly smaller than those without considering the time-dependent effect model,and as the extraction time increases,the viscoelastic elements make the coal body denser in the creep constitutive. With the increase of extraction time,the time-dependent effect of deep coal seam becomes more obvious, and the difference increases gradually between the simulation results of porosity and permeability considering time-de- pendent effect or not. The time-dependent simulation results are in good agreement with the field data and are more in line with the actual evolutionary characteristics. At the same time,as the distance from the center of the borehole de- creases,the permeability shows an increasing trend,while the pressure shows a decreasing trend. When the extraction time is 1 d,the permeability is large and the gas pressure is small near the center of the borehole. At different extrac- tion times,when the extraction time gradually increases,the permeability gradually increases at the same position,and the gas pressure gradually decreases. When the extraction time increases from 1 d to 30 d,the permeability increases by nearly 1. 4 times near the center of the borehole,the gas pressure decreases by nearly 3. 8 times,and the evolution of permeability and gas pressure tends to balance in the model.