We present a minimal see-saw model based on an extension of the standard model (SM) which includes an additional U(1), with gauge charge $B - \frac{3}{2} (L_��+ L_��)$. Requirement of anomaly cancellation implies the existence of two right-handed singlet neutrinos, carrying this gauge charge, which have normal Dirac couplings to $��_��$ and $��_��$ but suppressed ones to $��_e$. Assuming the U(1) symmetry breaking scale to be 10$^{12-16}$~GeV, this model can naturally account for the large (small) mixing solutions to the atmospheric (solar) neutrino oscillations.

14 pages, latex, no figures