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Interfaces impede heat flow in micro/nanostructured systems. Conventional theories for interfacial thermal transport were derived based on bulk phonon properties of the materials making up the interface without explicitly considering the atomistic interfacial details, which are found critical to correctly describing thermal boundary conductance (TBC). Recent theoretical studies predicted the existence of localized phonon modes at the interface which can play an important role in understanding interfacial thermal transport. However, experimental validation is still lacking. Through a combination of Raman spectroscopy and high-energy resolution electron energy-loss spectroscopy (EELS) in a scanning transmission electron microscope, we report the first experimental observation of localized interfacial phonon modes at ~12 THz at a high-quality epitaxial Si-Ge interface. These modes are further confirmed using molecular dynamics simulations with a high-fidelity neural network interatomic potential, which also yield TBC agreeing well with that measured from time-domain thermoreflectance (TDTR) experiments. Simulations find that the interfacial phonon modes have obvious contribution to the total TBC. Our findings may significantly contribute to the understanding of interfacial thermal transport physics and have impact on engineering TBC at interfaces in applications such as electronics thermal management and thermoelectric energy conversion.