In order to study the shock initiation of the fragment on the covered explosive, the equivalent diameter and velocity of the fragment were obtained through theoretical calculations, and the critical criterion for the shock initiation of explosive was obtained by combining the Held criterion. Existing experimental data were used to verify the correctness of the criterion, and the simulation comparison using AUTODYN software was performed to obtain the critical initiation velocity of fragments with different materials. The simulation results show that errors of the critical initiation velocity of the covered explosive obtained by numerical simulation and theory are less than 2%, and the calculated results are basically consistent with the experimental data.