  We study the vacuum stability in the anomaly mediated supersymmetry (SUSY)
breaking models with massive neutrinos. It is shown that, because of the
seesaw-induced mass terms for neutrinos, the true vacuum has a large negative
cosmological constant provided that the vacuum where we now live has an
(almost) vanishing cosmological constant. Although the quantum transition into
the true vacuum from our false vacuum is highly suppressed, the thermal
transition at high temperatures may not be neglected because of the thermal
excitations. However, we find that the thermal transition is, in fact,
negligibly small and hence the anomaly mediation models are cosmologically
safe. Thus, we conclude that the reheating temperature T_R could be very high
(e.g. T_R >> 10^10 GeV) in the anomaly mediation models even with the
seesaw-induced mass terms for neutrinos.
