Titanium has excellent biocompatibility and good corrosion resistance and is extensively used in dental implants and denture bases. However, pure titanium lacks the strength for use in dental prostheses that require relatively high strength. We developed 15 different types of Ti-Nb-Cu alloys and investigated their alloy phases and mechanical properties, including tensile and yield strength, elongation after fracture, and Vickers hardness. The alloy phases of Ti-8%Nb-2%Cu and Ti-13%Nb-2%Cu were α + β, while those of Ti-5%Nb-5%Cu and Ti-10%Nb-5%Cu were α + Ti2Cu. The tensile strength and hardness of these alloys were significantly higher than those of titanium; however, their elongation was less. In particular, the yield strength of these alloys was more than twice that of titanium. These differences in mechanical properties are attributable to solid-solution strengthening and precipitation strengthening. Other compositions with an alloy phase of α + β + Ti2Cu or β + Ti2Cu had high hardness but not high strength. These results suggest that the Ti-8%Nb-2%Cu, Ti-5%Nb-5%Cu, Ti-13%Nb-2%Cu, and Ti-10%Nb-5%Cu alloys can be applied to dental prostheses, which are subject to very high forces from accessories such as long-span bridges, clasps, implant-retained superstructures, and narrow-diameter implants.