Important　tasks　in　cavity　quantum　electrodynamics　include　the　generation　and　control　of　quantum　states　of　spatially　separated　particles　distributed　in　different　cavities.　An　interesting　question　in　this　context　is　how　to　prepare　entanglement　among　particles　located　in　different　cavities,　which　are　important　for　large-scale　quantum　information　processing.　We　here　consider　a　multi-cavity　system　where　cavities　are　coupled　to　a　superconducting　(SC)　qubit　and　each　cavity　hosts　many　SC　qubits.　We　show　that　all　intra-cavity　SC　qubits　plus　the　coupler　SC　qubit　can　be　prepared　in　an　entangled　Greenberger-Horne-Zeilinger　(GHZ)　state,　by　using　a　single　operation　and　without　the　need　of　measurements.　The　GHZ　state　is　created　without　exciting　the　cavity　modes;　thus　greatly　suppressing　the　decoherence　caused　by　the　cavity-photon　decay　and　the　effect　of　unwanted　inter-cavity　crosstalk　on　the　operation.　We　also　introduce　two　simple　methods　for　entangling　the　intra-cavity　SC　qubits　in　a　GHZ　state.　As　an　example,　our　numerical　simulations　show　that　it　is　feasible,　with　current　circuit-QED　technology,　to　prepare　high-fidelity　GHZ　states,　for　up　to　nine　SC　qubits　by　using　SC　qubits　distributed　in　two　cavities.　This　proposal　can　in　principle　be　used　to　implement　a　GHZ　state　for　an　arbitrary　number　of　SC　qubits　distributed　in　multiple　cavities.　The　proposal　is　quite　general　and　can　be　applied　to　a　wide　range　of　physical　systems,　with　the　intra-cavity　qubits　being　either　atoms,　NV　centers,　quantum　dots,　or　various　SC　qubits.