We propose an efficient entanglement concentration protocol (ECP) for nonlocal three-atom systems in an arbitrary unknown less-entangled W state, resorting to the Faraday rotation of photonic polarization in cavity quantum electrodynamics and the systematic concentration method. In the first step of the present ECP, one party in quantum communication performs a parity-check measurement on her two atoms in two three-atom systems for dividing the composite six-atom systems into two groups. In the first group, the three parties will obtain some three-atom systems in a less-entangled state with two unknown coefficients. In the second group, they will obtain some less-entangled two-atom systems. In the second step of the ECP, the three parties can obtain a subset of three-atom systems in the standard maximally entangled W state by exploiting the above three-atom and two-atom systems. Moreover, the preserved systems in the failed instances can be used as the resource for the entanglement concentration in the next round. The total success probability of the ECP can therefore be largely increased by iterating the entanglement concentration process several rounds. The distinct feature of our ECP is that we can concentrate arbitrary unknown atomic entangled W states via photonic Faraday rotation, and thus it may be universal and useful for entanglement concentration in future quantum communication network.