Abstract: Through the observation of the shapes of the coal samples after crushing and screening, it is found that the shape of a small part of the cinder is spherical and flat, while the shape of most of the cinder is circular column or rectangular.The time-varying characteristics of diffusion coefficient in the process of cinder gas emission were analyzed, on this basis, a mathematical model of gas diffusion for circular column cinder based on time-varying diffusion coefficient was established, the corresponding analytical solutions were derived by using methods of mathematical physics. The analytical solution of the mathematical model of coal cinder gas diffusion in circular column shape was verified by experimental test and compared with that of the model for the diffusion of coal cinder gas in spherical shape.The results show that the analytical solution of the model for the diffusion of coal cinder gas in circular column shape can better reflect the characteristics of the cinder gas emission, it has wide applicability and can be used to fit test data, it also provides theoretical basis for the research of gas content determination method in underground coal mine.