Crystal structures and shape memory properties of Ti-rich Ti52Ni23Cu25 (at.%) ribbon annealed at 450°C for 10 min and 1 h were investigated by X-ray diffraction and dynamic mechanical analyzer. As-spun ribbon was full amorphous and its crystalline peak temperature is 455.4°C. The annealed ribbon is crystallized with strong preferential (110)-B2 orientation. It shows a well-defined shape memory effect and the transformation hysteresis for the annealed ribbon under an external load in the range of 3-9 N is about 38.5°C. With annealing time increasing from 10 min to 1 h, the maximum of transformation strain under the external stress decreases from 1.93% to 1.7%. The temperature dependence of the external stress increases from 0.3 N/°C to 0.43 N/°C. The residual plastic strain is up to about 0.4% at a load of 9 N.