The structural properties of Tix-Nb1-x (x=0.25, 0.5, 0.75) alloy systems under high pressure and temperature are investigated by first-principles calculations. The calculated lattice parameters of several Tix-Nb1-x alloy systems are consistent with the pre-existing experimental data and other theoretical data. Through the fitting of the energy-volume (E-V) curve, we draw a conclusion that the Nb0.75Ti0.25 and Nb0.5Ti0.5 are energetically favored to be in body-center cubic structures, but Nb0.25Ti0.75 alloys to be in hexagonal cubic structure. The elastic properties and elastic modulus of the stable Nb0.75Ti0.25, Ti0.5Nb0.5 and Ti0.75Nb0.25 alloy structures are also computed.