Fragment velocity characteristics of warheads are key issues in the field of explosion technology and protection. However, the fragment velocity characteristics of a warhead with a hollow core under asymmetrical initiation are rarely touched. In this work, the effects of the diameter of the hollow core on the fragment velocities of warheads under asymmetrical initiation were investigated by experimentally verified numerical simulations. The results showed that the fragment velocity-time curves exhibited a second time acceleration due to the collision of the shock/detonation wave and/or that of the detonation products. For warheads under symmetrical initiation, the second time acceleration becomes stronger, and then becomes slightly weaker with the increase of the diameter of the hollow core, due to the combined effects of bigger hollow core and less explosive charge mass. For warheads under asymmetrical initiation, the second time acceleration becomes more obvious with the increase of the diameter of the hollow core, because the larger shaped charge efficiency enhances the collision of the detonation products. A modified formula was proposed to predict the initial fragment velocity in the aiming direction of a warhead with a hollow core under asymmetrical initiation. Experimentally verified numerical simulations were then used to verify the formula and the results showed that the new formula could predict the velocity very well. This work could offer a good reference for the design of tunable effects warheads and aimable warheads.