  We study the thermal leptogenesis in the scenario where the standard model is
extended to include one $SU(2)_{L}$ triplet Higgs boson, in addition to three
generations of the right-handed neutrinos. And in the model we introduce the
coupling between the Quintessence and the right-handed neutrinos, the triplet
Higgs boson, so that the light neutrino masses vary during the evolution of the
universe. Assuming that the lepton number asymmetry is generated by the decays
of the lightest right-handed neutrino $N_{1}$, we find the thermal leptogenesis
can be characterized by four model independent parameters. In the case where
the contribution of the triplet Higgs to the lepton asymmetry is dominant, we
give the relation between the minimal $M_{1}$ and the absolute mass scale
$\bar{m}$ of the light neutrinos, by solving the Boltzmann equations
numerically. We will also show that with the varying neutrino masses, the
reheating temperature can be lowered in comparison with the traditional thermal
leptogenesis.
