We　propose　a　superconducting　qutrit-resonator　chain　model,　and　analytically　work　out　forms　of　its　topological　edge　states.　The　existence　of　the　zero-energy　mode　enables　one　to　generate　a　state　transfer　between　two　ends　of　the　chain,　accompanied　with　state　flips　of　all　intermediate　qutrits,　based　on　which　N-body　Greenberger-Horne-Zeilinger　(GHZ)　states　can　be　generated　with　great　robustness　against　disorders　of　coupling　strengths.　Three　schemes　of　generating　large-scale　GHZ　states　are　designed,　each　of　which　possesses　the　robustness　against　loss　of　qutrits　or　of　resonators,　meeting　a　certain　performance　requirement　of　different　experimental　devices.　With　experimentally　feasible　qutrit-resonator　coupling　strengths　and　available　coherence　times　of　qutrits　and　resonators,　it　has　a　potential　to　generate　large-scale　GHZ　states　among　dozens　of　qutrits　with　a　high　fidelity.　Further,　we　show　the　experimental　consideration　of　generating　GHZ　states　based　on　the　circuit　QED　system,　and　discuss　the　prospect　of　realizing　fast　GHZ　states.