In our previous DWF calculation with the Wilson gauge action at β = 6.0 (a −1 ≃ 1.9 GeV) on a 16 3 × 32 × 16 lattice, we found that g A had a fairly strong dependence on the quark mass. A simple linear extrapolation of g A to the chiral limit yielded a value that was almost a factor of two smaller than the experimental one. Here we report our recent study of this issue. In particular, we investigate possible errors arising from finite lattice volume, especially in the lighter quark mass region. We employ a RG-improved gauge action (DBW2), which maintains very good chiral behavior even on a coarse lattice (a −1 ≃ 1.3 GeV), in order to perform simulations at large physical volume (> (2fm) 3 ). Our preliminary results suggest that the finite volume effect is significant.The nucleon (iso-vector) axial charge g A is a particularly interesting quantity. We know precisely the experimental value g A = 1.2670(35) from neutron beta decay. Deviation of this quantity from unity, in contrast to the vector charge, g V = 1, reflects the fact that the axial current is only partially conserved in the strong interaction while the vector current is exactly conserved. However neither lattice-QCD nor any model calculation have successfully reproduced this value. Thus, the calculation of g A is an especially relevant test of the chiral properties of DWF in the baryon sector. In addition, calculation of g A is an important first step in studying polarized nucleon structure functions since g A = ∆u − ∆d where p, s|q f γ 5 γ µ q f |p, s = 2s µ ∆q f with s 2 = −1 and s · p = 0.We follow the standard practice [1] for the calculation of g V and g A . We define the three-point functions for the relevant components of the local vector current Jwhere Γ = V (vector) or A (axial) with P V = (1 + γ 4 )/2 and P A = P V γ i γ 5 . We use the nucleon interpolating operator N = ε abc (u T a Cγ 5 d b )u c . For the axial current, the three-point function is averaged over i = 1, 2, 3. The lattice estimates of vector and axial charges can be derived from the ratio between two-and three-point functionswhereRecall that in general lattice operators O lat and continuum operator O con are regularized in different schemes. The operators are related by a renormalization factorThis implies that the continuum value of vector and axial charges are given byIn the case of conventional Wilson fermions, the renormalization factor Z A is usually estimated in perturbation theory (Z A differs from unity because of explicit symmetry breaking). For DWF, the conserved axial current receives no renormalization. This is not true for the lattice local current. An important advantage with DWF, however, is that the lattice renormalizations, Z V and Z A , of the local currents are the same [2] so that