The transition from G1 phase to S phase in the cell cycle is regulated by G1/S checkpoint, which can arrest the G1 progression when DNA-damage occurred. However, it was reported that G1 arrest was not induced when DNA-damage occurred at late G1 phase. This finding implies that G1/S checkpoint cannot detect the DNA-damage on late G1 phase. The inadequate regulation of G1/S checkpoint to cell cycle progression produces serious effects on both the cellular homeostasis and genetic stability. In this paper, to verify the inadequate regulation of G1/S checkpoint, we constructed a novel mathematical model (proposed model), which integrated G1/S checkpoint with p53-dependent DNA-damage pathway, and simulated a dynamic behavior of G1/S transition involving DNA-damage. The hot issue of the study is that the simulation results of the proposed model with/without DNA-damage can qualitatively realize the biological findings such that G1/S checkpoint cannot detect the DNA-damage on late G1 phase.