  Charged lepton flavor violation (CLFV) represents a clear new physics (NP)
signal beyond the standard model (SM). In this work, we investigate CLFV
processes $l_j^-\rightarrow l_i^- \gamma$ utilizing mass insertion
approximation(MIA) in the minimal supersymmetric extension of the SM with local
B-L gauge symmetry (B-LSSM). The MIA method can provide a set of simple
analytic formulae for the form factors and the associated effective vertices,
so that the movement of the CLFV decays $l_j^-\rightarrow l_i^- \gamma$ with
the sensitive parameters will be intuitively analyzed. Considering the SM-like
Higgs boson mass and the muon anomalous dipole moment (MDM) within $4\sigma$,
$3\sigma$ and $2\sigma$ regions, we discuss the corresponding constraints on
the relevant parameter space of the model.
