  In this paper, the lepton flavor violating $\tau^- \to \mu^-
V^0(V^0=\rho^0,\phi,\omega)$ decays are studied in the framework of the two
Higgs doublet model(2HDM) III. We present a computation of the the $\gamma-$,
$Z$ penguin and box diagrams contributions, and make an analysis of their
impacts. Our results show that, among the $\gamma-$ penguins, the penguins with
neutral Higgs in the loop are very larger than those with charged Higgs in the
loop. We find that the model parameter $\lambda_{\tau\mu}$ is tightly
constrained at the order of $O(10^{-3})$ and the branching ratios of these
decays are available at the experiment measure. With the high luminosity, the B
factories have considerable capability to find these LFV processes. On the
other hand, these processes can also provide some valuable information to
future research and furthermore present the reliable evidence to test the 2HDM
III model.
