  We propose a model of Dirac neutrino masses generated at one-loop level. The
origin of this mass is induced from Peccei-Quinn symmetry breaking which was
proposed to solve the so-called strong CP problem in QCD, therefore, the
neutrino mass is connected with the QCD scale, $\Lambda_{\rm QCD}$. We also
study the parameter space of this model confronting with neutrino oscillation
data and leptonic rare decays. The phenomenological implications to leptonic
flavor physics such as the electromagnetic moment of charged leptons and
neutrinos are studied. Axion as the dark matter candidate is one of the
byproduct in our scenario. Di-photon and Z-photon decay channels in the LHC
Higgs search are investigated, we show that the effects of singly charged
singlet scalar can be distinguished from the general two Higgs doublet model.
