Abstract: The coefficient c(A) required for O(a) improvement of the axial current in lattice QCD with N-f = 3 flavors of Wilson fermions and the tree-level Symanzik-improved gauge action is determined non-perturbatively. The standard improvement condition using Schrodinger functional boundary conditions is employed at constant physics for a range of couplings relevant for simulations at lattice spacings of approximate to 0.09 fm and below. We define the improvement condition projected onto the zero topological charge sector of the theory, in order to avoid the problem of possibly insufficient tunneling between topological sectors in our simulations at the smallest bare coupling. An interpolation formula for c(A) (g(0)(2)) is provided together with our final results.