In this study, we investigate the lepton flavor violation (LFV) of Z gauge boson decaying into two different flavor charged leptons \(\varvec{Z\rightarrow } \varvec{l}_{\varvec{i}} \varvec{l}_{\varvec{j}}\) ( \(\varvec{Z\rightarrow \tau \mu }\) , \(\varvec{Z\rightarrow \tau e}\) and \(\varvec{Z\rightarrow \mu e}\) ). This work is performed in the framework of the constrained minimal supersymmetric standard model (CMSSM) which is extended by the type-III seesaw mechanism. By considering constraints from the current experimental bounds on neutrino and supersymmetric particle masses, we calculate the branching ratios of the LFV of \(\varvec{Z}\) boson decays. The numerical results are found to be \(\varvec{1.30 \times {10}}^{\varvec{-9}}\) for both the \(\varvec{\tau \mu }\) and \(\varvec{\tau e}\) decay channels and \(\varvec{6.40 \times {10}}^{\varvec{-10}}\) for the \(\varvec{\mu e}\) channel. After applying the constraints from the experimental bounds on the radiative two body decays \(\varvec{l}_{\varvec{i}}\varvec{\rightarrow } \varvec{l}_{\varvec{j}} \varvec{\gamma }\) , the branching ratios of the LFV of \(\varvec{Z}\) boson decays get an additional suppression of \(\varvec{10}^{\varvec{-3}}\) for the \(\varvec{\tau \mu }\) and \(\varvec{\tau e}\) decay channels and \(\varvec{10}^{\varvec{-8}}\) for the \(\varvec{\mu e}\) channel. Our prediction of the branching ratios is several orders of magnitude below the current experimental bounds.
