  Within framework of the $\mu$ from $\nu$ Supersymmetric Standard Model
($\mu\nu$SSM), exotic singlet right-handed neutrino superfields induce new
sources for lepton-flavor violation. In this work, we investigate some
lepton-flavor violating processes in detail in the $\mu\nu$SSM. The numerical
results indicate that the branching ratios for lepton-flavor violating
processes $\mu\rightarrow e\gamma$, $\tau\rightarrow\mu\gamma$ and
$\mu\rightarrow3e$ can reach $10^{-12}$ when $\tan\beta$ is large enough, which
can be detected in near future. We also discuss the constraint on the relevant
parameter space of the model from the muon anomalous magnetic dipole moment. In
addition, from the scalars for the $\mu\nu$SSM we strictly separate the
Goldstone bosons, which disappear in the physical gauge.
