  We propose a minimal type II seesaw model by introducing only one
right-handed neutrino besides the $SU(2)_{L}$ triplet Higgs to the standard
model. In the usual type II seesaw models with several right-handed neutrinos,
the contributions of the right-handed neutrinos and the triplet Higgs to the CP
asymmetry, which stems from the decay of the lightest right-handed neutrino,
are proportional to their respective contributions to the light neutrino mass
matrix. However, in our minimal type II seesaw model, this CP asymmetry is just
given by the one-loop vertex correction involving the triplet Higgs, even
though the contribution of the triplet Higgs does not dominate the light
neutrino masses. For illustration, the Fritzsch-type lepton mass matrices are
considered.
