In order to optimize the design of single fragment warhead, the ultimate penetration velocities of 0.16 g tungsten balls penetrating class III, IV Kevlar and 2 mm thick LY12CZ hard aluminum target are respectively 729 m/s, 746.2 m/s and 379.3 m/s by experiment. The ultimate penetration velocities of tungsten balls of different masses, such as 0.16 g, 0.2 g, 0.25 g, 0.3 g and 0.35 g, penetrating 2 mm thick LY12CZ hard aluminium plate are respectively 380 m/s, 363 m/s, 355.5 m/s, 337.5 m/s and 333.5 m/s by numerical simulation and the ultimate penetration velocities of tungsten balls penetrating Class III, IV Kevlar are calculated by the principle of specific kinetic energy invariance. According to the relation between the ultimate penetration velocities and the masses of tungsten balls, it can be concluded that the most suitable mass of the tungsten ball fragment is 0.2 g~0.25 g for single fragment warhead.