As a major greenhouse gas, carbon dioxide (CO2) causes climate warming and weather changes. On the basis of CO2 disposal/storage in salt caverns in this study, a new carbon cycle model is proposed, which provides a new way for carbon capture and storage. The safety and suitability evaluation of CO2 disposal/storage in bedded rock salt caverns in China was carried out. Long-term disposal (Time ≥1000 years), medium-term disposal (several hundred years), and short-term storage (0–30 years) were studied to meet permanent geological isolation of carbon and temporary carbon cycle. The results show that: 1) For long-term and medium-term disposal/storage, it is feasible to carry out permanent geological isolation at proper depth and operating pressure. 2) For short-term storage, the stability of CO2 and CH4 storage in bedded rock salt has a little difference by controlling the operating pressure constant withdrawal-injection cycle. However, the stored CO2 has a much larger storage density and working density than the stored CH4. 3) If dozens of such caverns can be used in a salt mine, the potential for disposal or storage is much considerable. Therefore, the utilization of CO2 storage in salt caverns also acts as an attractive way of carbon neutralization and carbon cycle.