Coalbed methane (CBM) is a relatively common unconventional natural gas, which has great exploitation value. Coal permeability is an important parameter that affects the production and production efficiency of CBM, which is mainly controlled by the sorption expansion/contraction strain and effective stress. To study the seepage characteristics of coal in the process of CBM production, we have used CH4 and CO2 as test gases separately and conducted comparative seepage tests of different gases under constant pore pressure conditions. At the same time, the elastic modulus reduction coefficient Rm has been introduced to characterize the sorption strain of coal, following which the permeability models suitable for different boundary conditions were derived according to the stress–strain relationship. Under the two gases, the new model could not only better reflect the law of coal sorption strain but also better reflect the relationship among effective stress, pore pressure, and coal permeability. Under the conditions of constant pore pressure, coal permeability was mainly controlled by effective stress; with the increase of effective stress, permeability decreased sharply initially and then gradually. Under the conditions of uniaxial strain and constant external stress, with an increase of pore pressure and Rm, the matrix sorption expansion strain increased, resulting in a narrowing of the seepage channel, and Rm indirectly inhibited permeability. At this point, coal permeability was mainly controlled by sorption expansion/contraction strain and effective stress. In addition, compared with other permeability models, the new permeability model possesses higher applicability both in theoretical mechanism and in data matching. The general change trend concerning coal permeability, determined by rebound pressure prb, was consistent with the test results, which further verified the applicability of the model. It is believed that the results of this study could provide a basis for subsequent research on the stress–strain–permeability relationship and for the study of efficient development of CBM.