We investigate the possibility of explanation for the muon anomalous magnetic moment $g_{\mu }-2$ 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 $g_{\mu }-2$. Stringent constraints due to lepton flavor violation $\mu \to e\gamma$, $\mu \text{−}e$ conversion and the electron anomalous magnetic moment $g_e-2$ are considered, and the results are compatible.