A simple scheme is presented for generating 2n-mode photon Greenberger-Horne-Zeilinger (GHZ) states with the interaction of a 2n-level atom with two n-mode cavities. In the proposed protocol, the 2n qubits are encoded in zero- and one-photon Fock states of 2n cavity modes. Because the interaction between the atom and cavity fields is resonant, the coupling strength can be relative strong. This will shorten the corresponding interaction time and thus reduce the effect of decoherence in experiment.