  A simple extension of Ma's approach in a scotogenic model is studied for the
purpose of simultaneously interpreting the neutrino data and the excess of muon
anomalous magnetic moment (muon $g-2$). The feasible minimal extension is to
add an $Z_2$-odd vector-like lepton doublet to the Ma's model. It is found that
in addition to the neutrino data, the strict constraints on the relevant
parameters are from the electroweak oblique parameters and the induced
lepton-flavor violation processes, such as $\ell_i \to \ell_j \gamma$ and
$\ell_i \to \ell^-_j \ell^-_j \ell^+_j$. Performing parameter scan, we
numerically demonstrate that when the constraint conditions are satisfied, the
muon $g-2$ of $O(10^{-9})$ can be achieved, where it can be expected that with
a $5\sigma$ observation, the Muon $g-2$ experiment at Fermilab can observe
$a_\mu \approx 13.31 \times 10^{-10}$ when the current experiment and the SM
errors are reduced by a factor of 4 and 2, respectively. Moreover, the
branching ratio of the $\tau \to \mu \gamma$ decay can match the Belle II
sensitivity of $O(10^{-9})$ with an integrated luminosity of 50 ab$^{-1}$.
