Precisely predicting the breakdown pressure of rock fractured by supercritical CO2 (SC-CO2) is one of the major challenges for optimize in-situ fracturing schemes. However, the influence of the infiltration effect caused by the unique properties of SC-CO2 on the fracture mechanism remains unclear, which may lead to inaccurate prediction of breakdown pressure. In this work, a pressurization rate model considering the physical properties changes of SC-CO2 is proposed to describe the relationship between the pressurization rate and the injection pressure of the fracturing fluid in a wellbore. Ultimately, combined with the pressurization rate model and the point stress criterion, a breakdown pressure model is established by considering the changes in the in-situ stress of wellbore surrounding rock, the fluid injection pressure inside the wellbore, and the pore pressure distribution. The results show that for permeable reservoirs, the breakdown pressure increases as the viscosity and injection rate of fracturing fluid increase, but it decreases with increasing rock permeability. The low viscosity and pressurization rate of SC-CO2 effectively increase the stress generated by the infiltration effect, which is negatively correlated with the breakdown pressure. In addition, the unique pressurization rate of SC-CO2 is the key factor for the abnormal breakdown pressure at different injection rates.