Not yet reviewed by Pith; the record is open.

In the Standard Model (SM), 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 $l_{j}^{-}\to l_{i}^{-}\gamma $ and $l_{j}^{-}\to l_{i}^{-}l_{i}^{-}l_{i}^{+}$ in LRSSM. Considering the constraints of the updated experimental datas, the numerical results show that the new contributions of $SU{{\left( 2 \right)}_{R}}$ gauge interaction and a large number of other new particles, such as ${{Z}^{'}}$ boson, double-charged Higgs-bosons in LRSSM can make significant contributions to the CLFV processes $l_{j}^{-}\to l_{i}^{-}\gamma $ and $l_{j}^{-}\to l_{i}^{-}l_{i}^{-}l_{i}^{+}$, which is much different from the ones predicted in other SUSY models. This work provide a theoretical base for finding the LFV phenomena in new physics.