  Atmospheric neutrino data strongly suggests a near-maximal \nu_\mu-\nu_{\tau}
mixing and also solar neutrino data can be nicely explained by another
near-maximal \nu_e-\nu_{\mu} or \nu_e-\nu_{\tau} mixing. We examine the
possibility that this bi-maximal mixing of atmospheric and solar neutrinos
arises naturally, while keeping U_{e3} and \Delta m^2_{sol}/\Delta m^2_{atm}
small enough, as a consequence of Abelian flavor symmetry. Two simple scenarios
of Abelian flavor symmetry within supersymmetric framework are considered to
obtain the desired form of the neutrino mass matrix and the charged lepton mass
matrix parameterized by the Cabibbo angle \lambda\approx 0.2. Future
experiments at a neutrino factory measuring the size of U_{e3} and the sign of
\Delta m^2_{32} could discriminate those scenarios as they predict distinctive
values of U_{e3} in connection with \Delta m^2_{sol}/\Delta m^2_{atm} and also
with the order of the neutrino mass eigenvalues.
