  A non-universal interaction, which involves only the third family leptons
induces lepton flavor violating couplings and contributes to the anomalous
magnetic moment of muon. In this paper, we study the effects of non-universal
interaction on muon (g-2) and rare decay $\tau \to \mu \gamma$ by using an
effective lagrangian technique, and a phenomenological $Z^\prime$ model where
$Z^\prime$ couples only to the third family lepton. We find that the deviation
from the theory can be explained and the induced $\tau \to \mu \gamma$ rate
could be very close to the current experimental limit. In the $Z^\prime$ model,
$M_{Z^\prime}$ has to be lighter than 2.6 TeV.
