Permeability is an important indicator of coalbed methane production. Previous classical theoretical permeability models under unconstrained boundary conditions have difficulty matching experimental results. Consideration of the actual cleat geometry can explain the non-equilibrium evolution of permeability to some extent, but the matrix swelling strain ignores the impact of damage effects. In this study, cleat damage is considered and the damage ratio is calculated. Damage as a function of strain can be solved iteratively by post-processing calculations using COMSOL Livelink with MATLAB software for correcting the permeability equation. Unlike conventional permeability models, this modified permeability model incorporates damage effects. Damage effects and matrix adsorption swelling are interactive and coupled processes. The main parameters controlling the matrix swelling strain are Young's modulus, Heterogeneous coefficient, gas injection pressure, Langmuir strain constant, and Poisson's ratio. Based on these parameters, eight working conditions are designed to compare the models without and with damage effects, and the numerical solutions of the two models are also compared with experimental data. The results show that the cleat damage model is valid better in coal permeability prediction than conventional models without damage effect. This is because the cleat damage inhibits fracture aperture rebound, which has a crucial influence on the evolution of permeability. Through this study, it is shown that the experimentally tested permeability results can indeed be explained by the impact of damage deformation on the cleat aperture.