  In this paper, we consider phenomenology of a model with an $L_\mu-L_\tau$
gauge symmetry. Since the muon couples to the $L_\mu-L_\tau$ gauge boson
(called $Z''$ boson), its contribution to the muon anomalous magnetic moment
(muon g-2) can account for the discrepancy between the standard model
prediction and the experimental measurements. On the other hand, the $Z''$
boson does not interact with the electron and quarks, and hence there are no
strong constraints from collider experiments even if the $Z''$ boson mass is of
the order of the electroweak scale. We show an allowed region of a parameter
space in the $L_\mu-L_\tau$ symmetric model, taking into account consistency
with the electroweak precision measurements as well as the muon g-2. We study
the Large Hadron Collider (LHC) phenomenology, and show that the current and
future data would probe the interesting parameter space for this model.
