We propose a hybrid plasmonic zeolitic imidazolate framework-8 (ZIF-8) nanostructure to achieve near-infrared dual-band sensing of trace amounts of volatile organic compound (VOC) gases via metal-organic framework patch array integrated on metal (Au) film. To achieve dual-band VOC gas sensing, two absorption peaks related to the surface lattice resonance (SLR) and surface plasmon polaritons (SPP) resonance are constructed in this plasmonic structure, to match the near-infrared absorption bands of methane and ethanol gas molecules respectively. For an 80 nm thick Au layer, the height and width of ZIF-8 patch and the gap between ZIF-8 patches are optimized to be 0.86, 0.925, and 0.43 μm. Then, this structure shows an SLR at 1392.64 and a SPP resonance at 1653.72 nm, which have peak intensities of 0.735 and 0.855, and the Q-values of 1435 and 253, respectively. Furthermore, the third resonance peak related to the Fano resonance is investigated and can be considered as a feasible alternative to calibrate the measurement without external references.