  Three singlet new Higgs superfields and right-handed neutrinos are added to
MSSM to obtain $U(1)_X$SSM model. Its local gauge group is $SU(3)_C\times
SU(2)_L \times U(1)_Y \times U(1)_X$. In the framework of $U(1)_X$SSM, we study
muon anomalous magnetic moment and lepton flavor violating decays
$l_j\rightarrow{l_i\gamma}(j=2,3;i=1,2)$ within the Mass Insertion
Approximation(MIA). Through the MIA method, we can find the parameters that
directly affect the analytical result of the lepton flavor violating decays
$l_j\rightarrow{l_i\gamma}$, which make our work more convenient. We want to
provide a set of simple analytic formulas for the form factors and the
associated effective vertices, that may be very useful for future
phenomenological studies of the lepton flavor violating decays. According to
the accuracy of the numerical results which the influence of different
sensitive parameters, we come to the conclusion that 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 clear signal of new physics(NP).
