We study the electrokinetic transport behavior of water molecules and ions in hydrophobic graphene nanochannels with variable surface charge densities and the interfacial water structure based on detailed molecular dynamics simulations. The interfacial water structure, described by the water density, hydrogen bonding, diffusion, distribution of the OH bond and dipole orientations, are strikingly influenced by the surface charge.We find anomalous electrostatic effects which depend on the distribution of counterions close to the surface, ion-specific effects and interfacial water structure. On a negatively charged surface, the attraction of Na + ions towards the graphene layer enhances the interfacial friction. In contrast, if the surface is positively charged, high surface charge density triggers an anomalous enhancement of electroosmotic flow, accompanied by an abrupt change of the interfacial water structure. At high surface charge densities, the mobility of the interfacial water at the positively charged surfaces is suppressed more strongly compared to the negatively charged surface. Our results imply new physics in electrokinetic transport when both negatively and positively charged surfaces are considered.