The effects of the addition of Cu on the phase transformation of Ti-Ni-Hf high-temperature shape memory alloy (SMA) have been studied. The experimental results shown that the Cu addition into the TiNiHf alloy slightly decreases the phase transformation temperatures, results in that the peak in the DSC curves splits into two peaks during cooling after thermal cycling and separates the martensite->R phase and R phase->parent phase transitions with the Cu content of 5 at.%.