  The latest measurements of the anomalous muon magnetic moment $a^{}_\mu
\equiv (g^{}_\mu - 2)/2$ show a $4.2\sigma$ discrepancy between the theoretical
prediction of the Standard Model and the experimental observations. In order to
account for such a discrepancy, we consider a possible extension of the
type-(I+II) seesaw model for neutrino mass generation with a gauged $L^{}_\mu -
L^{}_\tau$ symmetry. By explicitly constructing an economical model with only
one extra scalar singlet, we demonstrate that the gauge symmetry
$U(1)^{}_{L^{}_\mu - L^{}_\tau}$ and its spontaneous breaking are crucially
important not only for explaining the muon $(g - 2)$ result but also for
generating neutrino masses and leptonic flavor mixing. Various phenomenological
implications and experimental constraints on the model parameters are also
discussed.
