Abstract: The permeability of coal seams in China is generally low. Meanwhile, during the coal seam mining process, the permeability is also affected by the coupling of effective stress, temperature and moisture. The permeability model of damaged, cracked and damaged coal bodies can effectively predict the changes in permeability and thereby guide gas drainage. From the perspective of coal matrix damage and fracture, this paper considers the synergistic effects of effective stress, temperature and moisture on the fracture development and permeability characteristics of coal body. By introducing the fractal theory to quantify the degree of damage, and combining the Langmuir adsorption equation, thermal expansion and moisture absorption strain equation, a permeability model of coal body with matrix damage and fracture under the coupling effect of multiple factors is constructed and verified. The results show that the fitting curve of the permeability model of matrix damaged and fractured coal under the multi-factor coupling effect constructed in this paper has a high degree of agreement with the experimental data under different gas pressures, temperatures, moisture contents and stress boundary conditions. This indicates the applicability and accuracy of the permeability model under the multi-factor coupling effect constructed in this paper under complex conditions. Through the sensitivity analysis of model parameters, it is concluded that the influence of plastic parameters on permeability is significantly greater than that of elastic parameters. The temperature and humidity parameters in the elastic stage change the degree of pore closure by controlling the expansion and contraction behavior of the matrix, achieving dynamic regulation of permeability. The mechanical parameters of the coal body and the adsorption deformation mainly regulate the permeability through the competitive relationship. The parameters of the plastic stage dominate the nonlinear changes through the damage fractal and fracture penetration scale effects. When the stress is loaded to the peak strength, the permeability of the coal body surges sharply. The model constructed in this paper can accurately describe the nonlinear evolution law of permeability with the coupling of multiple factors, precisely predict the changes of coal seam permeability under different mining conditions, and provide theoretical support for gas drainage.