We investigate the possibility of explanation for the muon anomalous magnetic moment ${g}_{\ensuremath{\mu}}\ensuremath{-}2$ in a left-right model with an inverse seesaw mechanism. We emphasize that the observed deviation from the Standard Model predictions can be accommodated in a large part of the parameter space of this class of models, where loops with massive neutrinos and charged Higgs boson as well as the weak $W$ boson contribute significantly to ${g}_{\ensuremath{\mu}}\ensuremath{-}2$. Stringent constraints due to lepton flavor violation $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$, $\ensuremath{\mu}\text{\ensuremath{-}}e$ conversion and the electron anomalous magnetic moment ${g}_{e}\ensuremath{-}2$ are considered, and the results are compatible.