  We explore muon anomalous magnetic moment (muon $g-2$) in a scotogenic
neutrino model with a gauged lepton number symmetry $U(1)_{\mu-\tau}$. In this
model, a dominant muon $g-2$ contribution comes not from an additional gauge
sector but from a Yukawa sector. In our numerical $\Delta \chi^2$ analysis, we
show that our model is in favor of normal hierarchy with some features. We
demonstrate one benchmark point, satisfying muon $g-2$ at the best fit value
$25.1\times10^{-10}$.
