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We propose a model for the vector-like lepton to explain the small muon massby a seesaw mechanism, based on lepton-specific two Higgs doublet models with alocal $U(1)'$ symmetry. There is no bare muon mass for a nonzero $U(1)'$ chargeof the leptophilic Higgs doublet, so the physical muon mass is generated due tothe mixing between the vector-like lepton and the muon after the leptophilicHiggs doublet and the dark Higgs get VEVs. In this scenario, the non-decouplingeffects of the vector-like lepton give rise to leading contributions to themuon $g-2$, thanks to the light $Z'$ and the light dark Higgs boson. We discussvarious constraints on the model from lepton flavor violation, electroweakprecision and Higgs data, as well as collider searches.

Seesaw lepton masses and muon $g-2$ from heavy vector-like leptons