To generate small neutrino masses radiatively, the Zee model introduces two
Higgs doublets and one weak-singlet charged Higgs boson to its Higgs secto
r. From analyzing the renormalization group equations, we determine the pos
sible range of the lightest CP-even Higgs boson (h) mass and the Higgs boso
n self-couplings as a function of the cutoff scale beyond which either some
of the coupling constants are strong enough to invalidate the perturbative
analysis or the stability of the electroweak vacuum is no longer guarantee
d. Using the results obtained from the above analysis, we find that the sin
glet charged Higgs boson can significantly modify the partial decay width o
f h --> gamma gamma via radiative corrections, and its collider phenomenolo
gy can also be drastically different from that of the charged Higgs bosons
in the usual two-Higgs-doublet models.