The finite element method （FEM） has algorithmic difficulties in describing fracture and friction， while the discrete element method （DEM） has difficulties in describing the structure response of explosives. Aiming at these problems， a three-dimensional numerical simulation combining FEM and DEM was established. The deformation of the outer metal shell of the explosive was simulated by FEM； the crack propagation and frictional heating inside the explosive were simulated by DEM； the decomposition heat release of the explosive was describe by the Arrhenius equation； and finally， a three-dimensional simulation of non-impact ignition of charge low-speed impact is realized. Taking Steven impact test as an example， the charge damage and ignition simulation of the brittle explosive PBX-2 under two impact conditions of ball head projectile and flat head projectile were carried out. The influence of the non-uniformity of the explosive was investigated. The history of load stress， crack distribution， temperature rise curve， ignition time and position， and velocity threshold of impact ignition were obtained. The random dispersion characteristics of impact ignition of ball head projectile and flat head projectile were analyzed. The simulation results based on the ignition mechanisms of explosive crack friction and self-reaction heat release are in good agreement with the reported experimental results.