Ti-Ni shape memory alloy is used for bio-medical and industrial fields even if Ni is a substance which has strong allergic nature and carcinogenicity to a human body, then, Ti-Ni alloy system is in a prohibition tendency in the medical field in Europe in recent years. Therefore, Ni-free shape memory alloy is desired in the near future medical field. In this research, we pay our attention to the Ti-Nb alloy which has shape memory as well as superelastic effects. The Ti-Nb fiber was fabricated by using the ark melting and nozzelless rapid solidification method. The fiber samples were used to investigate the following characteristics relating with shape memory effect, that is to say, (1) cross sectional microstructure observation, (2) DSC(phase transformation temperature changes), (3) temperature-shape recovery relationship. Moreover, heat-treated effect on shape recovery phenomena was observed in comparison with the starting bulk material. Finally, the fundamental discussion to correlate the rapid-solidification process condition with the characteristic of Ti-Nb shape memory alloy for bio-medical engineering application was conducted.