  In a supersymmetric extension of the Standard Model(SM) where baryon and
lepton numbers are local gauge symmetries (BLMSSM), we investigate the charged
lepton flavor violating (CLFV) processes $Z\rightarrow l_i^{\pm}l_j^{\mp}$
after introducing the new gauginos and the right-handed neutrinos. In this
model, the branching ratios of $Z\rightarrow l_i^{\pm}l_j^{\mp}$ are around
($10^{-8}\sim10^{-10}$), which approach the present experimental upper bounds.
We hope that the branching ratios for these CLFV processes can be detected in
the near future.
