In this paper, the lepton flavor violating $tau^- to mu^-PP (PP=K^+K^-,K^0bar{K}^0,pi^+pi^-,pi^0pi^0)$ 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 mode
l parameter $|lambda_{taumu}|$ 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 $|lambda_{taumu}|$. 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.
