  To solve the $\mu$ problem and generate three tiny neutrino masses in the
MSSM, the $\mu$ from $\nu$ Supersymmetric Standard Model ($\mu\nu$SSM)
introduces three singlet right-handed neutrino superfields, which lead to the
mixing of the Higgs doublets with the sneutrinos. The mixing affects the
lightest Higgs boson mass and the Higgs couplings. The present observed 95\% CL
upper limit on signal strength of the 125 GeV Higgs boson decay $h\rightarrow
Z\gamma$ is 6.6, which still is plenty of space to prove the existence of new
physics. In this work, we investigate the signal strength of the 125 GeV Higgs
boson decay channel $h\rightarrow Z\gamma$ in the $\mu\nu$SSM. Besides, we
consider the two-loop electroweak corrections of muon anomalous magnetic dipole
moment (MDM) in the model, which also make important contributions compared
with one-loop electroweak corrections.
