We investigated the structural stabilities of the intermetallics and the solid-state phase transformations induced by lattice vibration effects in the Al–Zr system by first-principles calculations. The calculated lattice parameters of all the phases and the phonon dispersion relations for pure Al and Zr are in good agreement with the experimental data. AlZr(oC8), Al4Zr5 (hP18), and Al3Zr5 (tI32) are predicted to be the high-temperature phases. To study the structural stabilities at high temperatures, the thermodynamic properties of the intermetallics are calculated via the linear response approach within the harmonic approximation. Thanks to the calculated enthalpies of formation at high temperatures, Al3Zr5 is predicted to be stabilized above 1163 K with respect to AlZr2 and Al2Zr3, in good agreement with the phase transformation temperature (1273 K) in the experimental phase diagram.