Hydroxylation of the rutile TiO$_2$ (110) surface has attracted much attention as the excess unpaired electrons introduced by hydroxyls play a critical role in surface chemistry and photocatalysis process of this material. In this work, based on density functional theory calculations with the Hubbard U correction, the electronic structures of the hydroxylated TiO$_2$ (110) surfaces have been studied. One interesting effect is found that the hydroxylation can elevate band edges of TiO$_2$, and thus can enhance its reducing power for photocatalysis. The underlying physical mechanism for such shifts of the band edges are associated with the electric dipoles arising from the hydroxyl groups on the surface. ; Comment: 4 figures