In this paper, we adopted a novel semi-analytical method to calculate the carbon geosequestration capacity of shale reservoir. Our methodology has the ability to calculate carbon geosequestration capacity of shales by considering Knudsen diffusion, molecular diffusion, Langmuir's adsorption, and stress-sensitivity of the permeability. Our model is more in line with the actual situations, allowing us to accurately estimate the carbon storage capacity by capturing the transient pressure solutions of the injection well. Additionally, the model verification in this paper shows that the error is 3%, indicating the reliability of the model. Sensitive analysis presents that the CO2 geosequestration capacity is proportional to fracture half-length and fracture conductivity. The change in the property for hydraulic fractures only affects the early period of the CO2 geosequestration process. For the adsorption coefficient, with the increase of the adsorption coefficient, the CO2 geosequestration capacity also become greater. This phenomenon has become more apparent with the continuous progress of the CO2 storage process.