In this paper, a nonlinear energy sink (NES) is designed and applied for the suppression of the friction-induced vibration (FIV) of a braking system. The equation of motion of the braking system, as well as the NES, is established by using the Lagrange equation. The nonlinear restoring force of the NES is realized by vertically paralleling two linear springs. The friction force between the wheel and the braking block is calculated by the Coulomb–Stribeck friction model. The variation of the wheel speed with the friction force is derived by the kinetic energy theorem. From the simulation, two-stage FIV systems are observed. The wheel speed decreases monotonically in the first stage and oscillates around 0 m/s in the second stage. The effects of the contact pressure and stiffness coefficient of the block on the FIV system are analyzed. By series connecting the NES to the braking block, the amplitude of FIV braking system can be reduced significantly in the first stage. Furthermore, the effects of the mass ratio between the block and the NES, and the damping coefficient of the NES on the FIV braking system are also discussed. This research can be helpful for the vibration suppression design of the braking system in vehicles.