Data set for the publication with the title 'Real-space imaging of an anisotropic atomic charge of σ-hole by means of Kelvin probe force microscopy'. An anisotropic charge distribution on individual atoms, such as σ-holes, may strongly affect the material and structural properties of systems. However, the spatial resolution of such anisotropic charge distributions on an atom represents a long-standing experimental challenge. In particular, the existence of the σ-hole on halogen atoms has been demonstrated only indirectly through the determination of the crystal structures of organic molecules containing halogens or via theoretical calculations, but its direct experimental visualization has not yet been reported . Here we demonstrate that Kelvin probe force microscopy with a properly functionalized probe can image the anisotropic charge of the σ-hole and of a quadrupolar charge of a carbon monoxide molecule. This achievement opens a new way to characterize biological and chemical systems where anisotropic atomic charges play a decisive role.