Over the last decades, numerous investigations have been conducted on Nitinol properties. However, the effects of alloying elements on Ni-rich NiTi alloys have been considered less. In this research, different effects of homogenization time and cooling rate on the behaviors of Ni-42.5wt%Ti-3wt%Cu alloy were evaluated. The mentioned alloy was fabricated by vacuum arc melting method. Three different homogenization times (half, one and two hours) and three cooling media (water, air and furnace) were selected. The microstructure and hardness were examined by means of optical and scanning electron microscope (SEM) equipped with an energy dispersive X-ray (EDX) analysis and hardness test, respectively. According to the microscopic investigations, no significant changes were observed after half an hour. However, results indicate that increasing time of homogenization leads to finer precipitations and a uniform distribution of them. The various cooling environments result in the formation of two types of precipitation phases. It was seen that in the high cooling rate, the majority of precipitations consisted of Ti2(Ni,Cu) while by decreasing cooling rate NiTiCu precipitates appeared too, which affect the hardness.