The tumor suppressor p53 can be activated by DNA damage and exhibits undamped pulses. Recent reports have demonstrated a non-threshold mechanism for p53 dynamics. However, no related theoretical studies have been proposed. Here, we constructed a refined DNA damage repair model that incorporated both intrinsic and extrinsic DNA lesions. We proposed that the basal DNA damage may trigger significant fractions of p53 pulses. We also reproduced the heterogeneity of p53 dynamics in experiments. The number of p53 pulses showed no correlations with DNA damage. We also replicated the linear correlation between DNA damage and the probability of igniting a pulse. Our model has unraveled the heterogeneous p53 responses.