  A natural extension of the standard model to accommodate massive neutrinos is
to introduce one Higgs triplet and three right-handed Majorana neutrinos,
leading to a 6 \times6 neutrino mass matrix. We show that three light Majorana
neutrinos (i.e., the mass eigenstates of \nu_e, \nu_\mu and \nu_\tau) are
exactly massless, if and only if M_L = M_D M^{-1}_R M^T_D exactly holds in this
seesaw model. We propose three simple Type-II seesaw scenarios with broken A_4
\times U(1)_X flavor symmetry to interpret the observed neutrino mass spectrum
and neutrino mixing pattern. Such a TeV-scale neutrino model can be tested in
two complementary ways: (1) searching for possible collider signatures of
lepton number violation induced by the right-handed Majorana neutrinos and
doubly-charged Higgs particles; and (2) searching for possible consequences of
unitarity violation of the 3\times 3 neutrino mixing matrix in the future
long-baseline neutrino oscillation experiments.
