  The $N$-qubit Greenberger-Horne-Zeilinger (GHZ) states are the maximally
entangled states of $N$ qubits, which have had many important applications in
quantum information processing, such as quantum key distribution and quantum
secret sharing. Thus how to distinguish the GHZ states from other quantum
states becomes a significant problem. In this work, by presenting a family of
the generalized Clauser-Horne-Shimony-Holt (CHSH) inequality, we show that the
$N$-qubit GHZ states can be indeed identified by the maximal violations of the
generalized CHSH inequality under some specific measurement settings. The
generalized CHSH inequality is simple and contains only four correlation
functions for any $N$-qubit system, thus has the merit of facilitating
experimental verification. Furthermore, we present a quantum phenomenon of
robust violations of the generalized CHSH inequality, in which the maximal
violation of Bell's inequality can be robust under some specific noises adding
to the $N$-qubit GHZ states.
