In the standard model, the charged lepton-flavor violation (CLFV) processes are forbidden, so the observation of CLFV represents a clear signal of new physics that goes beyond the standard model. In this work, we focus on the CLFV processes lj−→li−γ and lj−→li−li−li+ in the left-right supersymmetric standard model (LRSSM). Considering the constraints of the updated experimental data, the numerical results show that the new contributions of SU(2)R gauge interaction and a large number of other new particles, such as the Z′ boson and double-charged Higgs bosons in LRSSM can make significant contributions to the CLFV processes lj−→li−γ and lj−→li−li−li+, which is much different from the ones predicted in other supersymmetry models. This work provides a theoretical base for finding the lepton-flavor violation phenomena in new physics. Published by the American Physical Society 2024