  We study the lightest Higgs boson decays $h\rightarrow MZ$ in the framework
of the $\mu$ from $\nu$ supersymmetric standard model ($\mu\nu$SSM), where $M$
is a vector meson $(\rho,\omega,\phi,J/\Psi,\Upsilon)$. Compared to the minimal
supersymmetric standard model (MSSM), the $\mu\nu$SSM introduces three
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. Compared to the standard model, the $\mu\nu$SSM can
give large new physics contributions to the decay width of $h\rightarrow MZ$ in
suitable parameter space, which may be detected by the HL-LHC or the other
future high energy colliders.
