  We propose a model having a gauged $SU(2)$ symmetry associated with the
second and third generations of leptons, dubbed $SU(2)_{\mu\tau}$, of which
$U(1)_{L_\mu-L_\tau}$ is an Abelian subgroup. In addition to the Standard Model
fields, we introduce two types of scalar fields. One exotic scalar field is an
$SU(2)_{\mu\tau}$ doublet and SM singlet that develops a nonzero vacuum
expectation value at presumably multi-TeV scale to completely break the
$SU(2)_{\mu\tau}$ symmetry, rendering three massive gauge bosons. At the same
time, the other exotic scalar field, carrying electroweak as well as
$SU(2)_{\mu\tau}$ charges, is induced to have a nonzero vacuum expectation
value as well and breaks mass degeneracy between the muon and tau. We examine
how the new particles in the model contribute to the muon anomalous magnetic
moment in the parameter space compliant with the Michel decays of tau.
