Abstract: Through analyzing the characteristics of waste rock in the coal mine, the gas diffusion law is studied. The mathematical model of gas diffusion is established, and the fluid dynamics features of gas migration and distribution are described. After increasing the air volume, the dynamic balance relationship between ventilation pressure in the heading face and the gas pressure inside the goaf is reflected. Using the conservation law of mass and nonlinear seepage equations, based on Fick diffusion law and the Brinkman equations, the gas diffusion and convection model are proposed to take into account the role of fluid pressure gradient and kinetic energy. Through the comparison of numerical simulation and experimental results, the mechanism of gas migration in goaf in heading face is studied. In conclusion, the mathematical model simulating the gas diffusion in goaf is considered to be effective and feasible, which can provide the theoretical basis for the gas diffusion and contribute to mine gas monitoring and safety management.