The geometric and spin-resolved electronic structure of a graphene-adsorbed Ni(111) surface has been investigated by density functional theory (DFT) calculations without and with a semiempirical long-range dispersion correction (DFT-D). DFT calculations with generalized gradient approximation (GGA) functional cannot predict well about the adsorption properties of graphene to the Ni(111) surface. While DFT-D calculations with the same GGA functional give reasonable values of the adsorption energy and layer distance from graphene to the substrate. The geometry of top-fcc is the most energetically favorable in all geometries. Strong hybridization of graphene with the ferromagnetic Ni substrate induces significant shift partially in graphene π states towards the Fermi level yielding spin polarization. The spin polarization is positive at the shallow levels of modified π states and slightly negative at the deeper levels of fundamental π states, which is indicated by the calculated spin density distributions and plane-averaged density of states at the vacuum side. The opposite spin polarization is consistent with our experimental result of spin asymmetry obtained by spin-polarized metastable-atom de-excitation spectroscopy measurements.