During the injection of CO2 into coalbed for geologic sequestration, CO2 is likely both adsorbed and dissolved in coals, and swells them slightly. When coal is swollen due to the adsorption and dissolution, the induced strain is relieved as the coal structure rearranges to a lower free energy state, causing coal damage and resulting in permeability change. This adsorption- and dissolution- induced coal damage is usually ignored in the permeability model, even though this kind of damage has been observed and detected in the past CO2 injection experiments. In a previous study we generated a sequence of coal permeability profiles from the “V” shape as observed in experiments through a newly dual-permeability model. Based on this work, in this paper, the dual-permeability model is extended to take the coal damage induced by gas adsorption and dissolution into account according to the principle of damage mechanics, and this model is used to examine the permeability evolution during the injections of different gases, including CO2, CH4 and N2, into coal specimen. Numerical simulation indicates that the model predicts well the permeability increase during the high injected gas pressure. In addition, since the highest gas adsorption into coal occurs for CO2, the coal permeability during CO2 injection decreases most pronounced, in contrast, the permeability reduction during N2 injection is the smallest. Also, it is confirmed that the adsorption-induced coal damage is dominated by tensile damage of coal during the injection of CO2.