  Recently, the ATLAS and CMS Collaborations measured the 125 GeV Higgs boson
decay to a pair of muons $h\rightarrow \mu \bar{\mu}$, which reported the
signal strength relative to the standard model (SM) prediction is $1.2\pm0.6$
and $1.19^{+0.40+0.15}_{-0.39-0.14}$, respectively. In this work, we
investigate the 125 GeV Higgs boson decay $h\rightarrow \mu \bar{\mu}$ at
one-loop level in the $\mu$ from $\nu$ Supersymmetric Standard Model
($\mu\nu$SSM). Compared to the SM prediction, the decay width of $h\rightarrow
\mu \bar{\mu}$ in the $\mu\nu$SSM can boost up about 10\%, considering the
constraint from the muon anomalous magnetic dipole moment.
