  A radiative seesaw model with an inert doublet dark matter is a promising
candidate which could explain the existence of neutrino masses, dark matter and
baryon number asymmetry of the Universe, simultaneously. In addition to these
issues, inflation should also be explained since the recent CMB observations
suggest the existence of the inflationary era at the early stage of the
Universe. Thus, we extend it by a complex scalar field with a specific
potential. This scaler could also be related to the neutrino mass generation at
a TeV scale. We show that the inflation favored by the CMB observations could
be realized even if inflaton takes sub-Plankian values during inflation.
