Shale gas resources are highly abundant in the world. They can provide sustainable energy supply and have the potential to reduce energy prices. Therefore, shale gas has become one of the most important resources for oil and gas exploration and production, especially in North America today. Adsorption and desorption of methane gas are some of the important physical and chemical processes involved in the accumulation, transport, and production of shale gas. The shale matrix will shrink or swell due to the desorption or adsorption of methane gas, which will impact the recovery of shale gas reservoirs. The main purpose of this investigation is to quantitatively ascertain how the adsorption of methane gas affects the volumetric changes of the shale matrix. Based on the adsorption potential theory, a modified Dubinin-Astakhov (D-A) equation was employed to describe the adsorption of supercritical methane gas on shale. Then, a coupled adsorption-strain model was established to investigate the volumetric strain of shale induced by the combined effects of methane gas adsorption and stress compression. The methane adsorption and the induced shale swelling were measured on a black shale sample from the Sichuan Basin at 303.15 K and pressure up to 10 MPa, and the proposed models were employed to interpret the experimental data. The results demonstrate that the proposed models show good applicability and provide a reliable prediction. The swelling moduli of shale samples were obtained by fitting the experimental data using the coupled adsorption-strain model. The results indicate that the swelling modulus of shale in this study is generally greater than that of coal. The calculated ratios of Young's modulus to the swelling modulus do not show great variation from shale to shale in this study, which is similar to coal. This study can be incorporated into the numerical simulation of the production process of shale gas reservoirs.