A scheme was proposed for implementing the entangled W state of three atoms trapped in distant cavities connected by single-mode fibers. The scheme is robust to atomic spontaneous decay, cavity decay and photon leaking out of the fiber due to that the atomic system, all the modes of cavity fields and fibers are only virtually excited. Compared to the previous schemes, the significant advantage is that the adiabatic passage is applied in the scheme. It does not need precise control of the Rabi frequency, pulse duration and is insensitive to moderate fluctuations of experimental parameters. In principle, the n-atom W state can be prepared by using such a method.