The electron band structure of graphene on SrTiO3 substrate has been investigated as a function of temperature. The high-resolution angle-resolved photoemission study reveals that the spectral width at Fermi energy and the Fermi velocity of graphene on SrTiO3 are comparable to those of graphene on a BN substrate. Near the charge neutrality, the energy-momentum dispersion of graphene exhibits a strong deviation from the well-known linearity, which is magnified as temperature decreases. Such modification resembles the characteristics of enhanced electron-electron interaction. Our results not only suggest that SrTiO3 can be a plausible candidate as a substrate material for applications in graphene-based electronics but also provide a possible route toward the realization of a new type of strongly correlated electron phases in the prototypical two-dimensional system via the manipulation of temperature and a proper choice of dielectric substrates.