The carbon dioxide geological storage is one of the most effective ways to slow down the earth's climate warming. The ideal location for storage is in the deep scrap mines. Because of the characteristics of the deep underground condition, the long-term mechanical stability must have close relationship with the geostress fields and permeability, whose development can determine and reflect the mechanical behaviors of carbon dioxide geological storage. The permeability of host rock is affected by existing joints and discontinuity surfaces. Furthermore, as the liquid carbon dioxide is injected into the geological storage, the injection pressure and buoyancy force will change the state of geostress obviously. In this paper, based on mechanical properties of the host rock (granite), coupled brittle shear constitutive model was adopted and the analysis module was implemented in software FLAC3D. Then, with the in situ survey of joints in the host rock and the monitoring of in situ geostress, the permeability characteristics and geostress inverse analysis were input in FLAC3D. At last, fluid-solid coupled model was used to analyze the seepage characteristics of each phase after the injection and long-term storage of liquid carbon dioxide. Therefore, the systematic analysis of the storage stability of carbon dioxide geological could be carried out.