The role of proximity contact with magnetic oxides is of particular interest from the expectations of the induced spin polarization and weak interactions at the graphene/magnetic oxide interfaces, which would allow us to achieve efficient spin-polarized injection in graphene-based spintronic devices. A combined approach of topmost-surface sensitive spectroscopy utilizing spin-polarized metastable He atoms and ab initio calculations provides us direct evidence for the magnetic proximity effect in the junctions of single-layer graphene and half-metallic manganite Lac(0.7)Sr(0.3)MnO(3) (LSMO). It is successfully demonstrated that in the graphene/LSMO junctions a sizable spin polarization is induced at the Fermi level of graphene in parallel to the spin polarization direction of LSMO without giving rise to a significant modification in the pi band structure.