  We investigate the way how the total mass sum of neutrinos can be constrained
from the neutrinoless double beta decay and cosmological probes with cosmic
microwave background (WMAP 3-year results), large scale structures including
2dFGRS and SDSS data sets. First we discuss, in brief, on the current status of
neutrino mass bounds from neutrino beta decays and cosmic constrain within the
flat $\Lambda CMD$ model. In addition, we explore the interacting neutrino
dark-energy model, where the evolution of neutrino masses is determined by
quintessence scalar filed, which is responsable for cosmic acceleration today.
Assuming the flatness of the universe, the constraint we can derive from the
current observation is $\sum m_{\nu} < 0.87$eV at the 95 % confidence level,
which is consistent with $\sum m_{\nu} < 0.68$eV in the flat $\Lambda CDM$
model. Finally we discuss the future prospect of the neutrino mass bound with
weak-lensing effects.
