To investigate the thermal safety of the base bleeding projectile, based on the two-step chemical reaction mechanism of ammonium perchlorate(AP)/hydroxyl-terminated polybutadiene(HTPB) base bleeding propellant, a two-dimensional unsteady state cook-off model of the base bleeding unit is built. The fast cook-off response characteristics of the base bleeding unit were analyzed under the conditions of the external heating rates of 1, 5 K·min^-1 and 10 K·min^-1, respectively. The results show that at heating rates of 1, 5 K·min^-1 and 10 K·min^-1, the first ignition points of the base bleeding propellant all occur near the outside end surface wall of the base bleeding propellant. The change in external heating rates has little impact on the ignition position of base bleeding propellant. With increasing the heating rate, the ignition time occurring cook-off response of base bleeding propellant reveals an exponential decay. At heating rates of 1, 5 K·min^-1 and 10 K·min^-1, the temperatures occurring cook-off response of AP/HTPB base bleeding propellant are 579.4, 574.0 K and 573.5 K, respectively. The effect of heating rateson the ignition temperature of base bleeding propellant is small.