To examine experimentally the kinetics of the reactive diffusion between solid-Cu and solid-Al, sandwich Al/Cu/Al diffusion couples were prepared by a diffusion-bonding technique and then isothermally annealed in the temperature range of T = 693-753 K for various times up to 336 h. Owing to annealing, compound layers of the gamma (1), delta, zeta (2), eta (2), and theta phases are formed between the Cu and Al specimens. The gamma (1), delta, zeta (2), eta (2), and theta phases are the only stable compounds at T = 693-753 K in the binary Cu-Al system. At each annealing time, the thickness of the theta phase is much greater than those of the delta, zeta (2), and eta (2) phases but smaller than that of the gamma (1) phase. Hence, the overall growth of the compound layers is governed by the gamma (1) and theta phases. The mean thickness of each compound layer is proportional to a power function of the annealing time. For the gamma (1) phase, the exponent m of the power function is 0.5 at T = 753 K. Such a relationship is called a parabolic relationship. As the annealing temperature T decreases, however, m gradually increases and then reaches to 0.66 at T = 693 K. On the other hand, for the theta phase, m is close to 0.5 at T = 723-753 K and becomes 0.42 at T = 693 K. In the gamma (1) and theta phases, grain growth occurs at T = 693-753 K. Thus, the layer growth of the theta phase is controlled by volume diffusion at T = 723-753 K but partially by boundary diffusion at T = 693 K. On the other hand, for the gamma (1) phase, volume diffusion is the rate-controlling process of the layer growth at T = 753 K, but interface reaction contributes to the rate-controlling process at T = 693-723 K. Consequently, the rate-controlling process varies depending on the annealing temperature in a different manner for each compound.