Lime is an important industrial raw material, which is widely used in iron- and steel-making, flue gas desulfurization, construction and papermaking industries. Lime is generally obtained by calcining limestone in a kiln, that is, limestone is heated and decomposed to generate lime and carbon dioxide (CO2). In the conventional lime calcination process because the fuel is burned in the shaft kiln, the CO2 released by the limestone decomposition is mixed with the flue gas, resulting in that the CO2 capture requires gas separation. The new lime calcination process using CO2 as a circulating carrier gas to heat the limestone particles can avoid the above mixing problem, thereby directly capturing the CO2 generated by the limestone decomposition, which is expected to reduce carbon emissions from lime production by approximately 70%. However, the new calcination process based on CO2 heating is quite different from the conventional calcination process. To understand the new calcination process and accurately design and optimize it, a mathematical model of the lime calcination process based on CO2 heating was established. Based on the model, a shaft kiln with a capacity of 200 t·d-1 was simulated and calculated, and the profiles in the kiln of key parameters such as the gas-solid temperature difference, the gas flow rate, the gas temperature, the particle surface temperature, the reacting interface temperature, and the conversion ratio in the shaft kiln were obtained. Besides, the influence of the three operating parameters (the feed gas temperature, the feed gas flow rate, and the radius of feeding limestone particle) on the calcination process was analyzed. It was founded that (1) the lower the feed gas temperature, the lower the final conversion ratio, the pintch temperature difference, and the tail gas temperature of the kiln, and the change trend of the final conversion ration and pintch temperature difference conforms to a quadratic polynomial law, and the change trend of the tail gas temperature conforms to a linear law, (2) the lower the feed gas flow rate, the lower the final conversion ratio, pintch temperature difference and tail gas temperature of the kiln, and the change trend of each parameter conforms to a quadratic polynomial law, and (3) the larger the radius of the feeding limestone particle, the lower the final conversion ratio of the kiln, the higher the tail gas temperature, the greater the pintch temperature difference, and the changing trends of various parameters conform to cubic polynomial laws. Compared with the feed gas temperature and the feed gas flow rate, the radius of the feeding limestone particle has a greater impact on the pintch temperature difference and the tail gas temperature when the final conversion ration changes in the same range.