The ignition characteristics and the law of hot-spot formation on composite explosive subjected to drop weight impact were investigated by using the coupled thermo-mechanical method, selecting the thermo-elastic-plastic material model from nonlinear dynamics finite element software ANSYS/LS_DYNA, and simulating chemical exothermic reaction of explosive in the heat generation rate and considering the exothermic reaction of composite explosive itself. The finite element model used to simulate impact sensitivities was built by taking comp.B explosives as a caculation example. The results show that the numerical simulation method is feasible to simulate the transient heat release and the fast rise of temperature in composite explosive. The high temperature hot-spot in comp.B explosive is easily formed with the increment of up impact plunger velocity. When the velocity of up impact plunger is 5 m·s^-1, the hot-spot temperature enhances, and at 0.7 ms the hot-spots close to or above the critical temperature are formed, and ignition reaction occurs. The calculated results provide the theoretical foundations to judge the explosive impact ignition.