Two theoretical models based on momentum conservation, energy conservation, and law of motion were constructed to predict the velocity of fragments driven by mild detonating fuse (MDF). In the models, it is assumed that the driven velocity includes two parts: instant velocity coming from the impact of metal sheath and velocity increment caused by detonation products. Two groups of experiments were designed and carried out to validate the models. The experiment results show that the model based on momentum method better describes the fragments driving process. Furthermore, a series of finite-element simulations using LS-DYNA3D were done to fully verify the model. The simulation results show that the assumption of the fragment velocity composed of instant velocity and velocity increment is reasonable. Both theoretical predictions and simulation results all indicate that instant velocity coming from the impact of the metal sheath accounts for majority (average 89%) of the final velocity, which shows that lead sheath plays a key role in the accelerating progress of fragment driven by MDF. As a result, a certain distance should be allowed for the lead sheath to be accelerated to make full use of the MDF. This research may relate to the design of linear pyrotechnic separation device in aerospace engineering.