The Segall-Mahan theory is employed to calculate both one and two longitudinal-optical (LO) phonon sidebands of free excitons of zinc oxide (ZnO) in a wide temperature range. The energy spacing from the zero-phonon line to 1 LO and 2 LO phonon sidebands deviates gradually from their characteristic LO phonon energy with increaseing the temperature. The experimental results are good agreement with the theoretical calculation. Only one adjustable parameter is taken into account in this calculation, which determines the range of values of the hole effective mass in ZnO.