It is well known that Shape Memory Alloys (SMAs) recover the original shapes after deformation when heated. SMAs also show excellent damping properties compared with other materials. In this study the attenuation property of NiTiCu alloy in the small strain region is investigated using the inverted torsion pendulum. As the temperature goes up, phase transformation from martensite into austenite occurs, when the extent of attenuation decreases. This nhenomenon is different frnm those of other materials.