We herein report that surface modification of metal halide perovskites using graphene would be beneficial to improving the energy conversion efficiencies of perovskite solar cells. The present first-principles calculations on MAPbI with a single vacancy created by removing either I, Pb or MA show that the I and Pb vacancies near the surface result in the formation of Pb-Pb and I-I dimers, respectively. They are predicted to yield mid-gap levels, and would degrade the energy conversion efficiency of perovskite solar cells through carrier trapping. The present calculations suggest that when the surface of MAPbI is covered with a graphene sheet, the formation of the carrier trapping dimers would be suppressed. The origin of the "healing effect" of graphene on the lattice defect is ascribed to electronic interactions on the surface, which prevent charge localization at the lattice defects beneath the surface.