Apoptosis, or called programmed cell death, is an inherent protective mechanism in the body. Mitochondrial apoptosis is inseparable from BCL-2 protein family. The tumor suppressor protein p53 can prevent the proliferation of cells with abnormal genetic information (including cancer cells) by regulating apoptosis. It has been reported that SIRT1 has an effect on p53-mediated apoptosis, theoretical models in this regard, however, are still scarce. Therefore, this work developed a mathematical model to simulate the roles of SIRT1 in p53-mediated apoptosis. We first investigated the apoptosis of this gene network under three stress modes. Then, the method of bifurcation analysis was used. In agreement with the experimental reports, the model showed that there is an optimal content of SIRT1, at which the cell’s apoptotic ability is strongest. This paper provided new insights about the SIRT1-p53 axis in tumorigenesis, and may be useful for clinical treatment.