125 GeV Higgs decay with lepton flavor violation in the $\mu\nu$SSM

Recently, the CMS and ATLAS Collaborations have reported direct searches for the 125 GeV Higgs decay with lepton flavor violation, $h\rightarrow \mu \tau$. In this work, we analyze the signal of the lepton flavour violating (LFV) Higgs decay $h\rightarrow \mu \tau$ in the $\mu$ from $\nu$ Supersymmetric Standard Model ($\mu\nu$SSM) with slepton flavor mixing. Simultaneously, we consider the constraints from the LFV decay $\tau \rightarrow \mu \gamma$, the muon anomalous magnetic dipole moment and the lightest Higgs mass around 125 GeV.