  In this paper, the lepton flavor violating $\tau^- \to \mu^-PP
(PP=K^+K^-,K^0\bar{K}^0,\pi^+\pi^-,\pi^0\pi^0)$ decays are studied in the
framework of the two Higgs doublet model(2HDM) III. We calculate these decays
branching ratios and get the bounds of model parameter $|\lambda_{\tau\mu}|$
from the experimental upper limits. Our results show that, the neutral Higgs
bosons have tree-level contributions to these decays. Among these decays, the
$\tau^- \to \mu^- K^+K^-$ decay is most sensitive to $|\lambda_{\tau\mu}|$. In
the existing parameters space, these decays could reach the measure capability
of B factory. These processes can provide some valuable information to future
research and furthermore present the reliable evidence to test the 2HDM III
model.
