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