As the strong light-matter interaction between molecular vibrations and mid-infrared optical resonant modes, vibrational strong coupling (VSC) has the potential to modify the intrinsic chemistry of molecules, leading to the control of ground-state chemical reactions. Here, by using quartz as an epsilon-near-zero (ENZ) substrate, we have realized VSC between organic molecular vibrations and mid-infrared plasmons on metallic antennas. The ENZ substrate enables sharp mid-infrared plasmonic resonances (Q factor ∼50) which efficiently couple to the molecular vibrations of polymethyl methacrylate (PMMA) molecules with prominent mode splitting. The coupling strength is proportional to the square root of the thickness of the PMMA layer and reaches the VSC regime with a thickness of ∼300 nm. The coupling strength also depends on the polarization of the incident light, illustrating an additional way to control the molecule-plasmon coupling. Our findings provide a new, to the best of our knowledge, possibility to realize VSC with metallic antennas and pave the way to increase the sensitivity of molecular vibrational spectroscopy.