Buckling restrained braces (BRBs) are now widely used in different seismic zones as lateral resisting systems due to their quasi-symmetric and stable cyclic behavior. These systems are capable of dissipating the energy of severe lateral loads while protecting the integrity of other components of the structure. The material selection for these damper components as the inner core element requires high ductility, low strength increase, and high energy dissipation ability. Therefore, designing BRB steel cores using auxetic metamaterials has been recently investigated and suggested in the field of structure protection. The behavior of these metamaterials is characterized by a negative Poisson’s ratio (NPR) and unique mechanical characteristics, including their shear resistance and high ability for energy absorption. In this paper, we seek to investigate the effect of auxetic behavior on the dissipative performance of BRB under cyclic loading. Two different types of BRB were numerically designed and modeled using the finite element program Abaqus. The numerical analysis results show stable hysteresis behavior in both specimens and good stress distribution along the inner auxetic core. In addition, a parametric study was conducted to further investigate the effect of the gap size between the auxetic core and the concrete encasement. The cyclic performance of a buckling restrained brace with an auxetic perforated core was assessed, and the outcomes of this numerical analysis provide a reasonable basis for applying an auxetic core in the field of structure protection.