Graphene on metal substrates often shows different electronic properties from isolated graphene because of graphene-substrate interactions. One needs to remove the metals with acids and then to transfer graphene to weakly interacting substrates to recover electrical properties inherent in graphene. This process is not easy and besides causes undesirable tears, defects, and impurities in graphene. Here, we report a method to recover the electronic structure of graphene from a strongly interacting Ni substrate by spontaneous Na intercalation. In order to characterize the intercalation process, the density-functional-theory calculations and angle-resolved photoemission-spectroscopy (ARPES) and scanning-tunneling-microscopy (STM) measurements are carried out. From the density-functional-theory calculations, Na atoms energetically prefer interface intercalation to surface adsorption for the graphene/Ni(111) surface. Unlike most intercalants, Na atoms intercalate spontaneously at room temperature due to a tiny diffusion barrier, which is consistent with our temperature-dependent ARPES and core-level photoemission spectroscopy, and with our submonolayer ARPES and STM results at room temperature. As a result of the spontaneous intercalation, the electronic structure of graphene is almost recovered, as confirmed by the Dirac cone with a negligible band gap in ARPES and the sixfold symmetry in STM.