Microstructures and shape memory characteristics of $Ti_{50}Ni_{20}Cu_{30}$ alloy strips fabricated by arc melt overflow have been investigated by means of XRD, optical microscopy and DSC. The microstructure of as-cast strips exhibited columnar grains normal to the strip surface. X-ray diffraction analysis showed that one-step martensitic transformation of B2-B19 occurred in the alloy strips. According to the DSC analysis, it was known that the martensitic transformation temperature ($M_s$) of B2 $ ightarrow$ B19 in $Ti_{50}Ni_{20}Cu_{30}$ strip is $57^{circ}C$. During thermal cyclic deformation with the applied stress of 60 MPa, transformation hysteresis and elongation associated with the B2-B19 transformation were observed to be $3.7^{circ}C$ and 1.6%, respectively. The as-cast strip of $Ti_{50}Ni_{20}Cu_{30}$ alloy also showed a superelasticity and its stress hysteresis was as small as 14 MPa. These mechanical properties and shape memory characteristics of the alloy strips were ascribed to B2-B19 transformation and the controlled microstructures produced by rapid solidification of the arc melt overflow process.