  We present a proposal for generation of a robust tripartite
Greenberger-Horne-Zeilinger state among three-individual neutral Rydberg atoms.
By modulating the relation between two-photon detuning and Rydberg interaction
strength $U_{ij}(r)$, an effective Raman coupling is obtained between the
hyperfine ground states $|F=2,M=2\rangle$ of three $^{87}$Rb atoms and the
Rydberg states $|rrr\rangle$ via the third-order perturbation theory. This
method is also capable of implementing a three-qubit controlled-phase gate with
each qubit encoded into the hyperfine ground states $|F=1,M=1\rangle$ and
$|F=2,M=2\rangle$. As an extension, we generalize our scheme to the case of
multipartite GHZ state and quantum gate in virtue of high-order perturbation
theory.
