  In a supersymmetric extension of the standard model with local gauged baryon
and lepton numbers (BLMSSM), there are new sources for lepton flavor violation,
because the right-handed neutrinos and new gauginos are introduced. In BLMSSM,
we study the charged lepton flavor violating processes $l_j\rightarrow
l_i+\gamma$ and $l_j\rightarrow 3l_i$ in detail. The numerical results show
that in some parameter space the branching ratios for charged lepton flavor
violating processes can be large enough to be detected in the near future.
