  We interpret the newly observed muon g-2 anomaly in the framework of a
leptonic Higgs doublet model with nearly degenerate neutrino masses and nearly
bi-maximal neutrino mixing. Useful constraints are obtained on the rates of
lepton-flavor-violating rare decays $\tau \to \mu \gamma$, $\mu \to e \gamma$
and $\tau \to e \gamma$ as well as the $\mu$-$e$ conversion ratio $R_{\mu e}$.
We find that $\Gamma (\mu \to e \gamma)$, $\Gamma (\tau \to e \gamma)$ and
$R_{\mu e}$ depend crucially on possible non-zero but samll values of the
neutrino mixing matrix element $V_{e3}$, and they are also sensitive to the
Dirac-type CP-violating phase. In particular, we show that $\Gamma (\tau \to
\mu \gamma)/m^5_\tau$, $\Gamma (\mu \to e \gamma)/m^5_\mu$ and $\Gamma (\tau
\to e \gamma)/m^5_\tau$ are approximately in the ratio $1: 2|V_{e3}|^2:
2|V_{e3}|^2$ if $|V_{e3}|$ is much larger than ${\cal O}(10^{-2})$, and in the
ratio $2 (\Delta m^2_{\rm atm})^2: (\Delta m^2_{\rm sun})^2:(\Delta m^2_{\rm
sun})^2$ if $|V_{e3}|$ is much lower than ${\cal O}(10^{-3})$, where $\Delta
m^2_{\rm atm}$ and $\Delta m^2_{\rm sun}$ are the corresponding mass-squared
differences of atmospheric and solar neutrino oscillations.
