Molecules made of identical nuclei of non-zero spin exist in nuclear-spin modifications, and the interconversion of these spin isomers is often forbidden for isolated states(1-3). The inter-conversion between the nuclear-spin modifications, however, is promoted by inhomogeneous magnetic fields, such as those present on the surfaces of magnetic materials(4). Nuclear-spin conversion on diamagnetic and insulating solid substances, on the other hand, is generally considered improbable. Here we present the observation of nuclear-spin flips of H-2 and D-2 occurring on amorphous solid water surfaces with time constants of 370(-140)(+340) s and 1,220(-580)(+2,980) s, respectively. To explain these unexpected conversion processes, we propose a model of electric-field-induced nuclear-spin flips. In this model, giant and inhomogeneous electric fields present on the ice surface(5) mix the electronic states of opposite parities by the Stark effect(6), and significantly enhance the spin-orbit couplings between the electronic singlet-triplet spin states of the molecules. By virtue of these effects, the intramolecular hyper-fine contact interaction induces the nuclear-spin conversion. This concept should have implications for controlling nuclear magnetization using external electric fields(7).