The nonlinear energy sink (NES) is a light-weighted device used for shock mitigation in dynamic structures through its passive targeted energy transfer (TET) mechanism. Here, a new design for the NES is introduced based on using an asymmetric NES force. This force is strongly nonlinear in one side of the NES equilibrium position, whereas it is either weakly nonlinear or weakly linear in the other side. This is achieved by introducing the asymmetric magnet-based NES in which the asymmetric nonlinear magnetic repulsive force is generated by two pairs of aligned permanent magnets. Consequently, this proposed design is found to provide a considerable enhancement in the shock mitigation performance compared with the symmetric stiffness-based NESs for broadband energy inputs.