  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 $B -
\frac{3}{2} (L_\mu + L_\tau)$. Requirement of anomaly cancellation implies the
existence of two right-handed singlet neutrinos, carrying this gauge charge,
which have normal Dirac couplings to $\nu_\mu$ and $\nu_\tau$ but suppressed
ones to $\nu_e$. 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.
