The primary objective of this study is to investigate the adsorption and surface diffusion of supercritical methane in shale. An adaptive Dubinin-Astakhov (ADA) model, with a term taking the adsorbed phase density, was introduced to interpret measured excess adsorption isotherms and obtain temperature-independent characteristic curves. The ADA model can also predict adsorption isotherms at different temperatures. Combining with the ADA model and the Maxwell-Stefan equation, a new model was developed to describe the surface diffusion of supercritical methane in shale. The model was successfully validated against experimental data. We also studied the effect of fugacity and temperature on the surface diffusion. With increasing temperature, the surface diffusion flux reaches a maximum and then decreases, which is the result of a trade off between the amount adsorbed and the effective Maxwell-Stefan surface diffusivity. The driving force for surface diffusion is the chemical potential gradient, which can be related to the gradient of fractional occupancy by a thermodynamic factor. The absolute adsorption isotherms of supercritical methane in shale are of Type I in the IUPAC classification scheme. At high feed fugacity, the adsorbed concentration at feed side approaches saturation. Further increasing the feed fugacity can hardly increase the driving force for the surface diffusion. But increasing temperature can increase the effective Maxwell-Stefan surface diffusivity, which leads to the increase of the surface diffusion flux.