  Recent data on $e^+/e^-$ and $\bar{p}$ cosmic rays suggest that dark matter
annihilate into the standard model (SM) particles through new leptophilic
interaction. In this paper, we consider a standard model extension with the
gauged $U(1)_{L_\mu - L_\tau}$ group, with a new Dirac fermion charged under
this U(1) as a dark matter. We study the muon $(g-2)_\mu$, thermal relic
density of the cold dark matter, and the collider signatures of this model.
$Z^{'}$ productions at the Tevatron or the LHC could be easily order of
$O(1)-O(10^3)$ fb.
