Titanium-nickel (Ti-Ni) shape memory alloys have been widely used for biomedical applications in recent years. However, it is reported that Ni is allergic and possibly carcinogenic for the human body. Therefore, it is desirable to develop new Ni-free Ti-based shape memory alloys for biomedical applications. In the present study, a new Ti-18Nb-5Mo-5Sn (wt.%) alloy, containing only biocompatible alloying elements, was designed with the aid of molecular orbital method and produced by vacuum arc melting. Both β and α″ martensitic phases were found to coexist in the alloy after ice-water quenching, indicating the martensitic transformation. The phase transformation temperatures of the Ti-18Nb-5Mo-5Sn alloy were Ms = 7.3 °C, Mf = −31.0 °C, As = 9.9 °C, and Af = 54.8 °C. Superelasticity was observed in the alloy at a temperature higher than the Af temperature. A totally recovered strain of 3.5 % was achieved for the newly designed Ti-based shape memory alloy with a pre-strain of 4 %.