  We calculate one-loop correction to the axial Ward-Takahashi identity given
by Furman and Shamir in domain-wall QCD. It is shown perturbatively that the
renormalized axial Ward-Takahashi identity is satisfied without fine tuning and
the ``conserved'' axial current receives no renormalization, giving $Z_A=1$.
This fact will simplify the calculation of the pion decay constant in numerical
simulations since the decay constant defined by this current needs no lattice
renormalization factor.
