The numerical simulation results of shock initiation performance of composition B explosive with cover board subjected to tungsten fragments with different number and distribution were presented. In order to study the fragment parameter effect on shock initiation of composition B explosive. Numerical simulation of different number and distribution tungsten fragments which impact on cover board and composition B explosive were conducted with AUTODYN software. The critical detonation velocity of composition B explosive was obtained by the "up-down" method. It is indicated the superposition of shock wave caused by that multi-fragments impact on composition B explosive at the same time or not has an obvious effect on the critical detonation velocity and detonation time. When multi-fragments impact on composition B explosive at the same time, the critical detonation velocity of shock initiation decrease with the fragment number increase. The initiation detonation velocity of composition B explosive impacted by six fragments at the same time is about of 65% comparer to the situation that the explosive is impacted by single fragment. While the explosive is impacted by multi-fragments at the same time, the initiation detonation velocity increases gradually with the distance of horizontal and uptightness orientation increase, and tends to a critical value of one fragment.