Molecular dynamics simulations are preformed to investigate the diffusion behaviour of Ag/Gu double-layer islands on Ag(111)/Cu(111) surfaces, showing that atoms of the top island usually diffuse into the lower island by exchange mechanism when they move to the verge of the lower island via a concerted motion. Compared to the Cu adatoms, the Ag adatoms can easily form a kind of stable compact cluster of hexagonal island during their diffusion processes, and this cluster make it possible that the decay rate of the top Ag island is considerably slower than that of the Cu island. In addition, we find that the exchange mechanism is predominant compared to the jumping process in the simple potential calculation. These simulation results are in agreement with previous experimental observations and theoretical calculations.