Captured CO₂ is in a subcritical state, whereas CO₂ deep underground is in a supercritical state because of the high geothermal heat and pressure. The properties of CO₂ can change rapidly at the critical point and in the near-critical region during the transportation and injection process. This study aims to identify the instabilities in the CO₂ flow in these regions, along with the causes and effects, during the transportation and injection process, and propose relevant design specifications. Thus, the critical points and near-critical region of CO₂ flow were numerically analyzed. The unstable region is presented in terms of temperature and pressure ranges, and the changes in the CO₂ properties in this region were analyzed. In the unstable region, the sudden change in density was similar to the density wave oscillation of a two-phase flow. The CO₂ stability map we obtained and the stability map of supercritical water show similar trends. Flow instability was also found to occur in standard CO₂ transportation pipelines. We demonstrate that flow instability in CO₂ transportation and injection systems can be avoided by maintaining the proposed conditions.