In this work, a modified model considering partial penetration and finite conductivity of hydraulic fractures is introduced to estimate the carbon sequestration capacity of depleted shale reservoir with multiple fractured horizontal well. Firstly, the conservation equations, initial conditions as well as boundary conditions for matrix, natural fractures and hydraulic fractures are deduced with the consideration of partial penetration, finite conductivity, CO2 diffusion, adsorption and seepage. Then, by means of Laplace transform, Pedrosa transform as well as Fourier transform, the pressure response in real domain is acquired. Finally, based on the pressure response of injection well, the influence of penetration degree combined with hydraulic fracture conductivity and hydraulic fracture half length on carbon storage capacity are analyzed, which were always ignored in the conventional methodologies. The results indicate that the penetration degree has significant impact on the early and mid-stage of carbon storage. With the increase of hydraulic fracture half length and conductivity, the influence of penetration degree decreases gradually. Compared with conventional methodologies, the modified model can provide more precise predictions for carbon storage capacity of shale reservoirs.