  In this paper, we study the lepton flavor violating decays of the
$l_j\rightarrow l_i \gamma\gamma$ (j=2, 3; i=1, 2) processes under the
$U(1)_X$SSM. The $U(1)_X$SSM is the addition of three singlet new Higgs
superfields and right-handed neutrinos to the minimal supersymmetric standard
model (MSSM). Based on the latest experimental constraints of $l_j\rightarrow
l_i \gamma\gamma$, we analyze the effects of different sensitive parameters on
the results and made reasonable predictions for future experimental
development. Numerical analysis shows that many parameters have a greater or
lesser effect on lepton flavor violation(LFV), but the main sensitive
parameters and sources leading to LFV are the non-diagonal elements involving
the initial and final leptons. This work could provide a basis for the
discovery of the existence of new physics (NP).
