The influences of applied pressure on the structure, mechanics, dislocation, and electronics properties of an FeTi hydrogen storage alloy are theoretically investigated via first-principles calculations. The lattice parameter ratio, elastic constant, Young’s modulus, bulk modulus, shear modulus, ductile/brittle, Poisson’s ratio, anisotropy, Cauchy pressure, yield strength, Vickers hardness and energy factor are discussed versus applied pressure. The results show that the FeTi alloy exhibits good mechanical stability under applied pressure between 0 and 50 GPa, and the mechanical properties are significantly improved under applied pressure, like the resistances to elastic, bulk, and shear deformations, the material ductility and metallicity, as well as Vickers hardness and yield strength. Moreover, the electronic structures reveal that the FeTi alloy has metallic properties and the structural stability of the FeTi hydrogen storage alloy is enhanced at high pressure. This work provides significant value for high-pressure applications of FeTi alloys in hydrogen storage and supply fields.