  $U(1)_X$SSM is the extension of the minimal supersymmetric standard
model(MSSM) and its local gauge group is $SU(3)_C\times SU(2)_L \times U(1)_Y
\times U(1)_X$. To obtain this model, three singlet new Higgs superfields and
right-handed neutrinos are added to MSSM. In the framework of $U(1)_X$SSM, we
study lepton flavor violating decays
$\tau\rightarrow{Pl}(P=\pi,~\eta,~\eta^\prime;~l=\mu,~e)$. According to the
latest experimental data of $\tau\rightarrow{Pe}$ and $\tau\rightarrow{P\mu}$,
the influence of different sensitive parameters on the results is analyzed to
make a reasonable prediction for future experiments. From the numerical
analysis, the non-diagonal elements which correspond to the generations of the
initial lepton and final lepton are main sensitive parameters and lepton flavor
violation(LFV) sources. This work can provide a basis for finding the existence
of new physics(NP).
