In this study, a Ni44.8Ti45.2Hf5Cu5 shape memory alloy was fabricated by vacuum arc-melting in a copper mold. The alloy was solution annealed at 1000 °C for 60 min and subsequently aged at a temperature range between 300 °C and 600 °C for different time intervals from 10 to 240 min. The alloy underwent a B2 ↔ B19′ one-stage martensitic transformation. The results showed that martensitic transformation temperatures increased with increasing aging temperature from 300 to 600 °C. Increasing transformation temperatures with aging temperature is considered to be due to the suppression of Ti2Ni-type precipitates at higher aging temperatures. Constant stress thermal cycling experiments were carried out under a tensile stress of 200 MPa. The results indicated that aging treatment at a proper temperature could improve the recoverable strain in the alloy. The solution-annealed Ni44.8Cu5Ti45.2Hf5 alloy showed a recoverable strain of 6%, while after aging at 300 °C for 60 min, a recoverable strain as high as 8% was obtained under 200 MPa. On the other hand, the irrecoverable strain in the alloy was not affected by aging treatment and remained almost constant at close to 1% for all conditions. Furthermore, two-way shape memory effect in Ni44.8Ti45.2Hf5Cu5 alloy was developed by tensile deformation of martensite with a training strain of 3%. After solution annealing, the alloy exhibited a two-way shape-memory strain of 1.8%. With increasing aging temperature, the two-way shape memory strain increases until it reaches a maximum value of 2.2% at 400 °C and then decreases with further increasing the aging temperature.