  We discuss a possibility to explain the excess of $h\to\mu\tau$ at one-loop
level. We introduce three generation of vector-like lepton doublet $L'$ and two
singlet scalars $S_{1,2}$ which are odd under $Z_2$, while all the standard
model fields are even under this discrete symmetry. We show that $S_1$ can be a
good dark matter candidate. We show that we can explain the dark matter relic
abundance, large part of the discrepancy of muon $g-2$ between experiments and
the standard model predictions, as well as the $h\to\mu\tau$ excess of $\sim 1$
%, while evading constraints from experiments of dark matter direct detection
and charged lepton flavor violating processes. We also consider prospects of
production of $S_2$ at LHC with energy $\sqrt{s}=14$ TeV.
