A (Ti50Ni38Cu12)93Nb7 alloy is fabricated by arc melting, forging and drawing. The microstructure, transformation behavior and mechanical properties were investigated by means of scanning electron microscope (SEM), differential scanning calorimeter (DSC), dynamic mechanical analyzer (DMA) and tensile test machine. SEM observation showed that the as cast alloy is composed of TiNiCu and Nb-rich phases. After drawing, the alloy showed single step transformations during heating and cooling within the whole annealing temperature range from 400 °C to 800 °C. With the increase of the annealing temperature, both the transformation temperatures and the damping capacity increased first and then decreased. The ultimate strength of the alloy after annealing at 400 °C is over 1500 MPa and the maximum elongation of the alloy after annealing at 800 °C is more than 20%.