  We report the current status of the on-going lattice-QCD calculations of
nucleon isovector axial charge, g_A, using the RBC/UKQCD 2+1-flavor dynamical
domain-wall fermion ensembles at lattice cutoff of about a^{-1}=1.4 GeV in a
spatial volume (L = 4.6 fm)^3. The result from the ensemble with m_\pi = 250
MeV pion mass, corresponding to the finite-size scaling parameter m_\pi L \sim
5.8, agrees well with an earlier result at a^{-1}=1.7 GeV, L = 2.8 fm, and
m_\pi = 420 MeV, with similar m_\pi L. This suggests the systematic error from
excited-state contamination is small in both ensembles and about 10-% deficit
in g_A we are observing is likely a finite-size effect that scales with m_\pi
L. We also report the result from the lighter, m_\pi = 170 MeV ensemble.
