To clarify the effect of pressure on a (TaNb)0.67(HfZrTi)0.33 alloy composed of a solid solution with a single body-centered-cubic crystal structure, we used first-principles calculations to theoretically investigate the structural, elastic, and electronic properties of this alloy at different pressures. The results show that the calculated equilibrium lattice parameters are consistent with the experimental results, and that the normalized structural parameters of lattice constants and volume decrease whereas the total enthalpy difference ΔE and elastic constants in-crease with increasing pressure. The (TaNb)0.67(HfZrTi)0.33 alloy exhibits mechanical stability at high pressures lower than 400 GPa. At high pressure, the bulk modulus B shows larger values than the shear modulus G, and the alloy exhibits an obvious anisotropic feature at pressures ranging from 30 to 70 GPa. Our analysis of the electronic structures reveals that the atomic orbitals are occupied by the electrons change due to the compression of the crystal lattices under the effect of high pressure, which results in a decrease in the total density of states and a wider electron energy level. This factor is favorable for zero resistance.