Shape memory alloys exhibit strong damping capacity owing to the formation and motion of internal interfaces during the hysteretic superelastic response. Here, we report large mechanical damping behaviors in a Co53V30.5Ga12Mn4.5 polycrystalline alloy. By using Mn substitution for V to strengthen the ferromagnetic coupling in association with the martensitic transformation, the thermal hysteresis in the Co53V30.5Ga12Mn4.5 alloy is enhanced to 31.1 K. Under a low compressive loading of 248 MPa, a large dissipated energy of 2.45 MJ m–3 and a high specific damping capacity (SDC) of 0.39 can be achieved. Moreover, a long-term cyclability of over 10,000 superelastic cycles with the SDC higher than 0.32 is also obtained. Developing high-performance damping materials with the integration of low driving stress, high damping capacity and long fatigue life is of great importance for damping applications.