Among intermetallic compounds, the shape memory alloy is generally characterized by a unique shape memory phenomenon, high strength and high damping. The high damping of shape memory alloys may be closely related to the thermomechanical internal friction caused by the dynamic interferences in the heavily developed twin martensites. In the present paper, we investigate the possibility of improvement of the mechanical damping in rapidly quenched melt-spun Ti 50Ni 50− x Cu x ( x = 0–15 at.%) alloys. Mechanical damping was increased clearly with increase in cooling rate, in which microstructures were changed from coarse dendrite to very fine columnar grains. Furthermore, the mechanical damping was also increased by a 973 K aging treatment.