The structure, elastic constant, Debey temperature and electron distribution of α-Ti2Zr under high pressure are presented by using first-principles pseudopotential method based on density functional theory in this paper. The calculated structural parameters at zero pressure are in agreement with experimental values. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We obtain the bulk modulus, Young’s modulus and Poisson’s ratio for α-Ti2Zr. The G and B at zero pressure are 101.2 and 35.6 GPa, respectively. The G/B value is relatively small and decreases with pressure increasing, showing that the α-Ti2Zr is rather ductile. The Debye temperature Θ=321.7 K is obtained by the average sound velocity based on elastic constants. We investigate anisotropies of the compressional wave and two shear waves. The acoustic velocities are obtained from elastic constants by solving Christoffel equation. The results indicate the strong anisotropy for α-Ti2Zr. Moreover, the pressure dependence of s→d electron transfer indicates that β-Ti2Zr will occur under high pressure.