Porous TiNiCu ternary shape memory alloys （SMAs） were successfully fabricated by powder metallurgy method. The microstructure, martensitic transformation behavior, damping performance and mechanical properties of the fabricated alloys were intensively studied. It is found that the apparent density of alloys decreases with increasing the Cu content, the porous Ti50Ni40Cu10 alloy exhibits wide endothermic and exothermic peaks arisen from the hysteresis of martensitic transformations, while the porous Ti50Ni30Cu20 alloy shows much stronger and narrower endothermic and exothermic peaks owing to the B2-B19 transformation taking place easily. Moreover, the porous Ti50Ni40Cu10 alloy shows a lower shape recovery rate than the porous Ti50Ni50 alloy, while the porous Ti50Ni30Cu20 alloy behaves reversely. In addition, the damping capacity （or internal friction, IF） of the porous TiNiCu alloys increases with increasing the Cu content. The porous Ti50Ni30Cu20 alloy has very high equivalent internal friction, with the maximum equivalent internal friction value five times higher than that of the porous Ti50Ni50 alloy.
