  We have built a lepton-specific next-to-minimal two-Higgs-doublet-portal
vector dark matter model. The vector dark matter in the hidden sector does not
directly couple to the visible sector, but instead annihilates into the hidden
Higgs bosons which decay through a small coupling into the CP-odd Higgs bosons.
In this model, the Galactic center gamma-ray excess is mainly due to the 2-step
cascade annihilation with $\tau$'s in the final state. The obtained mass of the
CP-odd Higgs $A$ in the Galactic center excess fit can explain the muon $g-2$
anomaly at the 2$\sigma$ level without violating the stringent constraints from
the lepton universality and $\tau$ decays. We show three different freeze-out
types of the dark matter relic, called (i) the conventional WIMP dark matter,
(ii) the unconventional WIMP dark matter and (iii) the cannibally co-decaying
dark matter, depending on the magnitudes of the mixing angles between the
hidden Higgs and visible two-Higgs doublets. The dark matter in the hidden
sector is secluded from detections in the direct searches or colliders, while
the dark matter annihilation signals are not suppressed in a general hidden
sector dark matter model. We discuss the constraints from observations of the
dwarf spheroidal galaxies and the Fermi-LAT projected sensitivity.
