We propose a scheme for generating maximally entangled states for three atoms trapped in three distant cavities connected by two identical single-mode fibers. During the operation, neither the atomic system nor the fibers are excited, which is important in view of decoherence. Under certain conditions, the probability of the excited cavities can be negligible. Taking advantage of adiabatic passage, the GHZ state can be generated deterministically, and the fidelity of entanglement is insensitive to fluctuation of experimental parameters. Compared to the previous schemes, the significant advantage of the proposed scheme is that each cavity can interact with the other two directly, which can avoid the effect of indirect interaction brought about using only local quantum operator and nonlocal resources.