  We perform a non-perturbative determination of the improvement coefficient
c_A to remove O(a) discretization errors in the axial vector current in
three-flavor lattice QCD with the Iwasaki gauge action and the standard
O$(a)$-improved Wilson quark action. An improvement condition with a good
sensitivity to c_A is imposed at constant physics. Combining our results with
the perturbative expansion, c_A is now known rather precisely for 1/a \gtrsim
1.6 GeV.
