The supercritical CO2 enhanced coalbed methane (ScCO2-ECBM) technology is still in the development stage, and many simulation experiments and theoretical studies related to ScCO2-ECBM are being improved. Previous research works have conducted many studies on the competitive adsorption of CO2 and CH4 in coal, but there is less research on the competitive adsorption of ScCO2 and CH4 and its impact on methane extraction characteristics. In this study, a permeability model considering the competitive effects of effective stress and adsorption swelling on permeability was established. Based on the assumed conditions and permeability evolution model, different injected pressure and initial methane pressure conditions were set to obtain quantitative results of the competitive adsorption of ScCO2 and CH4, permeability changes, and CH4 production. By obtaining the competitive adsorption relationship between ScCO2 and CH4, we analyzed the evolution law of permeability and its impact on CH4 production. It was found that ScCO2 has a stronger competitive adsorption capacity, and the competitive adsorption capacity of ScCO2 and CH4 is more sensitive to injected pressure. Under two different conditions, it was found that the higher the injected pressure or injected differential pressure, the higher the initial permeability. However, due to the greater sensitivity of the competitive adsorption capacity of ScCO2 and CH4 to injected pressure, the greater the injected pressure in the later stage, the greater the decrease in permeability, resulting in a situation where the permeability at an injected pressure of 10 MPa is lower than that at an injected pressure of 8 MPa. A simple comparison was made between gaseous CO2 and ScCO2, and it was found that although injecting ScCO2 has a stronger adsorption swelling capacity that affects permeability changes, its stronger adsorption capacity can effectively displace methane and higher injected pressure, injected temperature, and advantages such as fracturing and extraction that are not yet reflected in the model. This study provides some guidance for numerical simulation of the ScCO2-ECBM process and the enhancement of coalbed methane extraction.