  Strong $CP$ problem is known to be solved by imposing Peccei-Quinn (PQ)
symmetry. However, domain wall problem caused by the spontaneous breaking of
its remnant discrete subgroup could make models invalid in many cases. We
propose a model in which the PQ charge is assigned quarks so as to escape this
problem without introducing any extra colored fermions. In the low energy
effective model resulting after the PQ symmetry breaking, both the quark mass
hierarchy and the CKM mixing could be explained through Froggatt-Nielsen
mechanism. If the model is combined with the lepton sector supplemented by an
inert doublet scalar and right-handed neutrinos, the effective model reduces to
the scotogenic neutrino mass model in which both the origin of neutrino masses
and dark matter are closely related. The strong $CP$ problem could be related
to the quark mass hierarchy, neutrino masses and dark matter through the PQ
symmetry.
