The integrity of the wellbore cement sheath plays a crucial role in the geological utilization and sequestration of carbon dioxide. Although high alumina cement (HAC) is a specialized cement with exceptional performance, additional research is required to assess its capability for long-term carbon dioxide sequestration. In this study, the effects of various corrosion conditions and pozzolanic materials on the corrosion of HAC were investigated by using the Gibbs energy minimization method. And the corrosion resistance of minerals was analyzed based on the multiphase chemical equilibrium theory. The results indicate that C3AH6 in HAC is the most susceptible to corrosion. As the temperature increases, more carbon dioxide is consumed for the complete reaction of the primary minerals in HAC. However, the corrosion of HAC is largely unaffected by system pressure. The high concentration of carbon dioxide in formation water accelerates mineral corrosion rates. In addition, the presence of Mg2+ and SO42− increases the formation of intermediate products during the corrosion of HAC, whereas the rate of mineral corrosion decreases as salinity increases. Fly ash can enhance the corrosion resistance of HAC during the initial stage of carbonization. Increasing the replacement ratio of fly ash to HAC reduces the generation of C3AH6 and increases the formation of C2ASH8. The corrosion resistance of each mineral is different, following the order: Al(OH)3 > C2ASH8 > C4AcH11 > C4Ac0.5H12 > C3AH6.