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 the muon anomalous magnetic moment (muon $g-2$). The feasible minimal extension is to add a $Z_2$-odd vectorlike 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 a parameter scan, we numerically demonstrate that when the constraint conditions are satisfied, the muon $g-2$ of $O\left({10}^{-9}\right)$ 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 $O\left({10}^{-9}\right)$ with an integrated luminosity of $50{\mathrm{ab}}^{-1}$.