The process of underground coal mining fractures the overlying strata and may provide storage and transportation space for gas by changing the roof rock permeability, which is released by pressure after mining. This paper adopts the experimental method of physical similarity simulation and combines the fractal theory to study the permeability characteristics of the fracture network after mining, and it establishes the fractal permeability equation of pressure-relief gas. The results of the study show that the fracture opening shows a positive correlation with the overburden permeability, whereas the tortuosity of the fracture shows a negative correlation with the overburden permeability. The shape of the high permeability area in the fracture network is found to be similar to the hat-shaped elliptical parabolic zone. In the process of permeability evolution, the key layer structure of the overburden rock is considered as the main factor that affects the trend of change in permeability. Furthermore, based on the above research results, this study developed a targeted design of high-level boreholes in the experimental face and reversed the permeability changes around the drainage borehole. The average error between the actual measured value and the theoretically calculated value is found to be 8.11%. The theoretical model and the permeability evolution law obtained from the research results can provide valuable references and insights into further research on the pressure-relief gas flow model in the goaf.