The dispersion distribution characteristics of prefabricated fragments from an improvised explosive device (IED) are essential in defense technology development. To improve warhead design, it is essential to predict a fragment’s velocity and dispersion distribution accurately. This paper investigates a fragment’s flying angle from a detonated warhead with a cylindrical charge under a one-end central detonation. A modified formula for calculating the fragment dispersion distribution at each axial position of the warhead was obtained based on experimental data and model analysis. The impacts of the following parameters on the flying angle were considered in the formula: ratio of charge mass to shell mass, charge diameter, axial sparse effect, and relative axial shell position. The formula was verified by experimentation to be suitable for wide applications using different validation samples. Theoretical calculations with the formula show good accuracy in predicting the flying angle of cylindrical-shell fragments, agreeing with experimental data. The proposed model meets the error requirements of engineering applications. This work provides a theoretical foundation for subsequent research on damage effectiveness and IED damage assessment.