  Lepton flavor violation (LFV) represents a clear new physics (NP) signal
beyond the standard model (SM). In this paper, we study LFV decays
$Z\rightarrow l^{\pm}_{i}l^{\mp}_{j}$ in the B-L Supersymmetric Standard
Model(B-LSSM). We calculate these processes separately in the mass eigenstate
basis and the electroweak interaction basis, and the latter adopt the mass
insertion approximation (MIA) method. The MIA clearly shows the effect of
parameters on the LFV decays $Z\rightarrow l^{\pm}_{i}l^{\mp}_{j}$ in the
analytic level, which provides a new way for us to analyze the LFV processes.
At the same time, the corresponding constraints from the LFV decays $l^{-}_{j}
\rightarrow l^{-}_{i} \gamma$ and $(g-2)_{\mu}$ are considered to analyze the
numerical results.
