Molecular hydrogen is classified into ortho (total nuclear spin I=1, rotational quantum number J=odd) and para (I=0, J=even) species. Although interconversion between the nuclear spin modifications is forbidden for isolated states, it is significantly promoted by inhomogeneous magnetic fields, such as those present on the surfaces of magnetic materials. Nuclear-spin conversion on diamagnetic and insulating solid substances, on the other hand, is generally considered improbable to date. Here we present our first observation of nuclear-spin flips of H2 occurring on diamagnetic amorphous-solid-water surfaces with time constants of ~410 s. To explain this unexpected conversion processes, we propose a novel model of electric-field-induced nuclear-spin flips. The conversion time estimated by this theory is in good agreement with the present experimental result.