  We study the nucleon axial charge in the chiral perturbation theory for a
mixed lattice action of Ginsparg-Wilson valence quarks and staggered sea
quarks. In particular, we investigate the lattice spacing $a^2$-dependence of
the neutron to proton axial transition matrix element. By using the known
low-energy constants (LEC's) and an estimated value of a new LEC which appears
in the calculation, we see a large lattice spacing effect on $g_A$.
