Interfaces play an important role in nanostructured structures, which have been widely employed to improve the efficiency of thermoelectric materials. Knowledge of how each specific phonon is scattered at an interface are desired to develop novel nanostructured materials with desired thermal properties. Phonon transmission across the interface consisting of silicon (Si) and germanium (Ge) is investigated by using lattice dynamics. It is found that there exists a critical phonon frequency for the thermal transport across the Si-Ge interface. When the phonon frequency is higher than 198 cm(-1), the phonon transmission coefficient is considerably low, which mean that phonons with higher frequencies contribute little to the thermal transport across the Si-Ge interface. While the phonon frequency goes lower than 198 cm(-1), the phonon transmission coefficient becomes much higher, inferring that phonons with lower frequencies contribute dominantly to the thermal conductance at the Si-Ge interface. This is helpful for understanding the underlying mechanisms of phonon transmission across a Si-Ge interface.