The aim of this work is to investigate the structure of water at the graphite(0001) surface by measuring the tunnel current as a function of the perpendicular distance by scanning tunnelling microscopy (STM). The tunnel currents were measurable in a range of about 0 to 0.3 nm, which is roughly equal to the width of a monolayer of water. The tunnel current was found to exhibit almost linear distance dependence. From these data the tunnelling barrier height as a function of distance was estimated and found to have a maximum at 0.2-0.25 nm from the surface. This is thought to be related to the positions of water molecule oxygens, enabling one to conjecture that there is a distinct water layer next to the highly oriented pyrolitic graphite (HOPG) surface. The topographic measurements suggest, however, that the water molecules are mobile within this surface layer because they cannot be observed directly : only the atomically resolved HOPG surface beneath the water layer was seen.