  $U(1)_X$SSM is the extension of the minimal supersymmetric standard model
(MSSM) and its local gauge group is $SU(3)_C\times SU(2)_L \times U(1)_Y \times
U(1)_X$. We study lepton flavor violating (LFV) decays
$Z\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$($Z\rightarrow e{\mu}$, $Z\rightarrow
e{\tau}$, and $Z\rightarrow {\mu}{\tau}$) and
$h\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$($h\rightarrow e{\mu}$, $h\rightarrow
e{\tau}$, and $h\rightarrow {\mu}{\tau}$), in this model. In the numerical
results, the branching ratios of $Z\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ are
from $10^{-9}$ to $10^{-13}$ and the branching ratios of
$h\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ are from $10^{-3}$ to $10^{-9}$, which
can approach the present experimental upper bounds. Based on the latest
experimental data, we analyze the influence of different sensitive parameters
on the branching ratio, and make reasonable predictions for future experiments.
The main sensitive parameters and LFV sources are the non-diagonal elements
corresponding to the initial and final generations of leptons, which can be
seen from the numerical analysis.
