A new shape memory alloy of Ferrous origin (Fe-Ni-Co-Al-Ta-B, referred to as FNCATB) is reported recently that shows huge Superelasticity in comparison with its earlier variants, such as Nitinol and Cu-Al-Be alloy, commonly employed in vibration damping applications. The performance of the FNCATB alloy based Superelastic damper is explored herein and compared with its conventional alternative. The optimal performance of the dampers is ensured by maximizing the equivalent damping, a closed form expression of which is derived based on the force–deformation behavior of the combined structure–damper system. The formulation closely follows that of conventional yield damper but with an additional term () characterizing the flag shaped hysteresis. The available experimental data from a cyclic test are fitted with the existing Auricchio model to describe the force–deformation hysteresis of FNCATB alloy. The dynamic response analysis of the structure–damper systems subjected to recorded seismic ground motions reveals the superior performance of this new damper in reducing the drift of the structure with almost identical base shear, experienced by the structure without damper. The primary constituent being ferrous, the FNCATB might be cost-effective, which is also supported by its less volume requirement, demonstrated herein.