Abstract: During extraction of coalbed methane, the reservoir will be in a non-equilibrium dynamic adjustment phase for a long period of time due to the high variability of fracture and matrix permeability properties. However, most of the current tests and permeability models only consider the effects of a certain fixed gas pressure, which greatly limits the study of reservoir gas flow under non-equilibrium condition. Therefore, based on the concept that the reservoir is a dual porous medium, and considering the effects of different pore pressures, desorption deformation and mechanical effects of matrix-fracture on the evolution of fracture aperture during the extraction process, a model is proposed to predict the reservoir permeability under variable stress states and validated through the field data. Then the model is substituted into the gas flow equation, and the pore pressure of matrix–fracture and the evolution of core permeability in time and space are studied separately by using the finite element software. The results show that during the core desorption: (1) The fracture gas pressure in the core is disturbed to a greater extent than the matrix gas pressure. (2) The gas pressure and permeability of matrix–fracture exhibit non-linear distribution along the core length. (3) The permeability of matrix–fracture varies in the same trend.