Visco-SCRAM model was applied to study on the influence of the initial crack on Octogen (HMX)-based polymer bonded explosive (PBX) ignition under low velocity impact. By means of the simulation of the standard low impact Steven test, the influence of the initial crack length and its distribution on the temperature rise and the hotspot formation was analyzed. The simulation results demonstrate that as the increment of the initial crack length, the friction work between the surfaces of the micro-cracks is strengthened, which brought in high temperature rise and further the hotspot is formed more easily. When the initial crack length is increased from 1mm to 3mm, the ignition impact threshold velocity is reduced from 45 m∙s^-1 to 38 m∙s^-1. Considering the heterogeneous initial crack, during the low velocity impact, the temperature rise region is obviously changed. Moreover, the hotspot formation is beneficial of the heterogeneous initial crack, and further it resulted in the reduction of the ignition impact threshold velocity. When the distribution of the initial crack follows the uniform distribution U(0.8, 1.2), the ignition impact threshold velocity is 36 m∙s^-1. When the distribution of the initial crack follows the normal distribution N(1, 0.115), the ignition impact threshold velocity is 31 m∙s^-1.