The potential energy surface of H2O-H2 is of great importance for quantum chemistry as a test case for H2O-molecule interactions. It is also required for a detailed understanding of important astrophysical processes, namely, the collisional excitation of water, including the pumping of water masers and the formation of molecular hydrogen on icy interstellar dust grains. We have calculated the interaction for H2O-H2 by performing both rigid-rotor (five-dimensional) and non-rigid-rotor (nine-dimensional) calculations using the coupled-cluster theory at the level of singles and doubles with perturbative corrections for triple excitations [CCSD(T)] with moderately large but thoroughly selected basis set. The resulting surface was further calibrated using high precision explicitly correlated CCSD(T)-R12 calculations on a subset of the rigid-rotor intermolecular geometries. The vibrationally averaged potential is presented in some details and is compared with the most recent rigid-rotor calculations. We explain, in particular, as to why vibrationally averaged rigid-rotor geometries are a better choice than equilibrium geometries. Our fit of the vibrationally averaged surface provides for the first time an accuracy of ~3 cm-1 in the van der Waals minimum region of the interaction. The overall accuracy of the nine-dimensional surface and fit is lower but remains of the order of 3%-4% of the anisotropy in the domain spanned by the vibrational functions.