  We study theoretical constraints on the parameter space under the conditions
from vacuum stability and triviality in the three-loop radiative seesaw model
with TeV-scale right-handed neutrinos which are odd under the $Z_2$ parity. In
this model, some of the neutrino Yukawa coupling constants can be of the order
of one. Requirement of strongly first order phase transition for successful
electroweak baryogenes is also prefers order-one coupling constants in the
scalar sector. Hence, it is important to clarify whether this model satisfies
those theoretical conditions up to a given cutoff scale. It is found that the
model can be consistent up to the scale above 10 TeV in the parameter region
where the neutrino data, the lepton flavor violation data, the thermal relic
abundance of dark matter as well as the requirement from the strongly first
order phase transition are satisfied.
