  Charged lepton flavor violating processes are forbidden in the standard model
(SM), hence the observation of charged lepton flavor transitions would
represent a clear signal of new physics beyond the standard Model. In this
work, we investigate some lepton flavor violating processes in the minimal
supersymmetric extension of the SM with local $B-L$ gauge symmetry (B-LSSM).
And including the corrections from some two loop diagrams to the anomalous
dipole moments (MDM) of muon, we discuss the corresponding constraint on the
relevant parameter space of the model. Considering the constraints from updated
experimental data, the numerical results show that, new contributions in the
B-LSSM enhance the MSSM predictions on the rates of $l_j-l_i$ transitions about
one order of magnitude, and also enhance the MSSM prediction on the muon MDM.
In addition, two loop electroweak corrections can make important contributions
to the muon MDM in the B-LSSM.
