  We present a Peccei-Quinn (PQ)-symmetric two-Higgs doublet model that
naturally predicts a fermionic singlet dark matter in the mass range 10 keV-1
GeV. The origin of the smallness of the mass of this light singlet fermion
arises predominantly at the one-loop level, upon soft or spontaneous breakdown
of the PQ symmetry via a complex scalar field in a fashion similar to the
so-called Dine-Fischler-Sredniki-Zhitnitsky axion model. The mass generation of
this fermionic Radiative Light Dark Matter (RLDM) requires the existence of two
heavy vector-like SU(2) isodoublets, which are not charged under the PQ
symmetry. We show how the RLDM can be produced via the freeze-in mechanism,
thus accounting for the missing matter in the Universe. Finally, we briefly
discuss possible theoretical and phenomenological implications of the RLDM
model for the strong CP problem and the CERN Large Hadron Collider (LHC).
