The non-linear responses of optical materials offer useful mechanisms for optical switching, novel optical sources, and harmonic frequency conversion. However, the non-linear response of traditional materials is usually extremely weak and requires high input power for excitation. In this study, we theoretically propose a scheme for enhancing the third harmonic generation (THG) efficiency and output power of layered graphene disks array by introducing a plasmonic antibonding state with enhanced oscillation strength due to plasmonic coupling. We verify that, the THG efficiency of a double-layer stacked graphene/SiO2 disk structure under relatively low input intensity can be significantly enhanced more than one order of magnitude with appropriate design, as compared with monolayer patterned graphene nanostructure. We also demonstrate that the THG efficiency can be further improved by optimizing the geometry parameters such as spacer distance and Fermi energy. Our results offer an effective mechanism for significantly improving THG efficiency in the mid-infrared and terahertz ranges, thereby paving the way for new frequency converters and modulators in optical communication and signal processing.