The covalent-like characteristics of hydrogen bonds offer a new perspective on intermolecular interactions. Here, using density functional theory and post-Hartree-Fock methods, we reveal that there are two bonding molecular orbitals (MOs) crossing the O and H atoms of the hydrogen-bond in water dimer. Energy decomposition analysis also shows a non-negligible contribution of the induction term. These results illustrate the covalent-like character of the hydrogen bond between water molecules, which contributes to the essential understanding of ice, liquid water, related materials, and life sciences.