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→ li±lj(±) after introducing new gauginos and right-handed neutrinos.In this model,the branching ratios of Z→li±lj(±) are around (10-8-10-10),which approach the present experimental upper bounds.We hope that the branching ratios for these CLFV processes can be detected in the near future.