Underground salt cavern is an effective geological body for CO₂ storage. The leakage of CO₂ along the weak interlayer of salt rock and the interface of salt layer and interlayer is the key to restrict the safe storage of CO₂ in underground salt cavern. A fluid-solid coupling mathematical model of CO₂ storage in bedded salt cavern gas storage was established based on the CO₂ salt cavern storage in Jintan area of Subei basin. On this basis, the leakage and migration law of CO₂ in salt rock and mudstone interlayer, as well as its influence on CO₂ safe storage, was analyzed. Meanwhile, the dynamic response characteristics of the permeability of salt rock and mudstone interlayer were discussed. The results show that the permeability is the key factor of CO₂ migration rate and leakage range in salt strata. Under the influence of permeability, the CO₂ migration rate and leakage range in the mudstone interlayer are greater than those in the salt rock. However, with the extension of the CO₂ storage time, the CO₂ migration rate and pressure increase in the salt rock and mudstone interlayer decrease in both, and tend to be stable as the CO₂ pressure spreads to the simulation boundary. The dynamic change of permeability is the result under the combined action of the negative effect of overlying formation pressure and the positive effect of the CO₂ pressure in salt strata, and affected by the mechanical properties of the salt rock and mudstone interlayer. When the CO₂ storage time is less than 3 years, the overlying formation pressure is the main controlling factor for the decrease of the salt rock permeability. With the extension of the CO₂ storage time, the influence of CO₂ pressure in the salt rock on the salt rock permeability gradually dominates, making the permeability of salt rock recover within the CO₂ influence range. Compared with salt rock, the elastic modulus of mudstone interlayer is smaller, while the influence of overlying formation pressure and CO₂ pressure on its permeability is more significant. The permeability of mudstone interlayer is generally higher than that of salt rock, and CO₂ mainly migrates and leaks along the mudstone interlayer. Therefore, the influence of mudstone interlayer should be fully considered during the site selection, construction and operation of CO₂ salt cavern storage, and proper protection and monitoring should be carried out to avoid CO₂ leakage along mudstone interlayer. Although the CO₂ storage pressure in the salt cavern has no significant effect on the migration rate and leakage range of CO₂ in salt strata, the high gas storage pressure increases the CO₂ pressure in salt strata within the CO₂ influence range, resulting in significant permeability recovery of the salt rock and mudstone interlayer, which indirectly affects the migration and leakage law of CO₂ in salt strata. Therefore, the influence of permeability and mechanical strength of salt rock and mudstone interlayer should be fully considered during the setting of CO₂ storage pressure.