The evolutions of system fidelity,atomic fidelity and cavity fidelity in the system of atoms interacting with coupled cavities were investigated considering two coupled cavities each containing one two-level atom and the atom interacts resonantly with cavity field.The temporal evolutions of system fidelity,atomic fidelity and cavity field fidelity were calculated and the influence of cavity-cavity coupling coefficient on the fidelity was discussed.The results show that when cavity-cavity coupling coefficient is small,the system fidelity and atomic fidelity all display irregular oscillations.When cavity-cavity coupling coefficient is greater than a certain value,they all display quasi-periodic oscillations.The fidelity of cavity field displays periodic oscillation,and its oscillation frequency increases with increase of cavity-cavity coupling coefficient.On the other hand,atomic fidelity is weakened,and the fidelity of cavity field is strengthened with increase of cavity-cavity coupling coefficient.