The latest experimental evidence indicates that acetylation of p53 at K164 (lysine 164) and K120 may induce directly cell apoptosis under severe DNA damage. However, previous cell apoptosis models only studied the effects of active and/or inactive p53, that is, phosphorylation/dephosphorylation of p53. In the present paper, based partly on Geva-Zatorsky et al. (2006) and Batchelor et al. (2008), we propose a new cell apoptosis network, in which p53 has three statuses, that is, unphosphorylated p53, phosphorylated p53, and acetylated p53. The time delay differential equations (DDEs) are formulated based on our network to investigate the dynamical insights of p53-induced cell apoptosis. In agreement with experiments (Loewer et al. (2010)), our simulations indicate that acetylated p53 accumulates gradually and then induces the proapoptotic protein Bax under enough DNA damage. Moreover, phosphorylated p53 oscillates and initiates cell repair during DNA damage.