Tantalum is used as a diffusion barrier in the superconducting Nb3Sn composite-wire manufactured by the bronze method. In order to examine the consumption behavior of the Ta barrier during annealing in the bronze method, the kinetics of the reactive diffusion between Ta and a bronze was experimentally observed using sandwich diffusion couples composed of Ta and a Cu-9.3Sn-0.3Ti alloy. The (Cu-Sn-Ti)/Ta/(Cu-Sn-Ti) diffusion couples were isothermally annealed at temperatures of T = 973-1053 K for various times up to t = 1462 h. Owing to annealing, Ta9Sn is formed as a uniform layer at the initial (Cu-Sn-Ti)/Ta interface in the diffusion couple, and gradually grows mainly toward Ta. The mean thickness of the Ta9Sn layer is proportional to a power function of the annealing time. However, the exponent of the power function is equal to unity at t < t (c) but smaller than 0.5 at t > t (c). Thus, the transition of the rate-controlling process for the growth of Ta9Sn occurs at t = t (c). The critical annealing time t (c) takes values of 1.83 x 10(6), 4.63 x 10(5), and 5.98 x 10(5) s at T = 973, 1023, and 1053 K, respectively. The growth of Ta9Sn is controlled by the interface reaction at the migrating Ta9Sn/Ta interface in the early stages with t < t (c) but by the volume and boundary diffusion across the Ta9Sn layer in the late stages with t > t (c). Due to the transition of the rate-controlling process, the growth rate is always much smaller for Ta9Sn than for Nb3Sn. As a result, Ta works as an effective barrier against the diffusion of Sn from the bronze to the Cu stabilizer in the superconducting Nb3Sn composite-wire.