[en] Renormalization constants of vector (Z_V) and axial-vector (Z_A) currents are determined non-perturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole improved clover quark action using the Schroedinger functional method. Non-perturbative values of Z_V and Z_A turn out to be smaller than the one-loop perturbative values by O(10%) at a^-1 ∼ 1 GeV. A sizable scaling violation of meson decay constants f_π and f_ρ observed with the one-loop renormalization factors remains even with non-perturbative renormalization