  The $\mu\nu$SSM, one of supersymmetric extensions of the Standard Model,
introduces three right-handed neutrino superfields to solve the $\mu$ problem
and violates lepton number. Within framwork of the $\mu\nu$SSM, we investigate
the lepton flavor violating (LFV) processes $Z\rightarrow l_i^\pm l_j^\mp$ with
slepton flavor mixing. Simultaneously, we consider the LFV processes
$l_j^-\rightarrow l_i^-\gamma$, $l_j^- \rightarrow l_i^- l_i^- l_i^+$ and muon
conversion to electron in nuclei.
