We report on the theoretical and the experimental investigations of the coherent phonon dynamics in sapphire crystal using the femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) technique.The temporal chirped white-light continuum (WLC) is used for the Stokes pulse,therefore we can perform the selective excitation of the phonon modes without using a complicated laser system.The expected quantum beat phenomenon is clearly observed.The theoretical formulas consist very well with the experimental results.The dephasing times of the excited phonon modes,the wavenumber difference,and the phase shift between the simultaneously excited modes are obtained and discussed.This work opens up a way to study directly high-frequency coherent phonon dynamics in bulk crystals on a femtosecond time scale and is especially helpful for understanding the nature of coherent phonons. We report on the theoretical and the experimental investigations of the coherent phonon dynamics in sapphire crystal using the femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) technique. Temporal temporal white-light continuum (WLC) is used for the Stokes pulse, therefore we can perform the selective excitation of the phonon modes without using a complicated laser system. The expected quantum beat phenomenon is clearly observed. The theoretical formulas very well with the experimental results. The dephasing times of the excited phonon modes, the wavenumber difference, and the phase shift between the successively excited modes are obtained and discussed. This work opens up a way to study directly high-frequency coherent phonon dynamics in bulk crystals on a femtosecond time scale and is especially helpful for understanding the nature of coherent phonons.