Using molecular dynamics simulations, we show a fine linear relationship between surface energies and microscopic Lennard-Jones parameters of super-hydrophilic surfaces. The linear slope of the super-hydrophilic surfaces is consistent with the linear slope of the super-hydrophobic, hydrophobic, and hydrophilic surfaces where stable water droplets can stand, indicating that there is a universal linear behavior of the surface energies with the water-surface van der Waals interaction that extends from the super-hydrophobic to super-hydrophilic surfaces. Moreover, we find that the linear relationship exists for various substrate types, and the linear slopes of these different types of substrates are dependent on the surface atom density, i.e., higher surface atom densities correspond to larger linear slopes. These results enrich our understanding of water behavior on solid surfaces, especially the water wetting behaviors on uncharged super-hydrophilic metal surfaces.