In this paper, a periodic metallic–dielectric nanorod array which consists of Si nanorods coated with 30 nm Ag thin film set in a hexagonal configuration is fabricated and characterized. The fabrication procedure is performed by using nanosphere lithography with reactive ion etching, followed by Ag thin-film deposition. The mechanism of the surface and gap plasmon modes supported by the fabricated structure is numerically demonstrated by the three-dimensional finite element method. The measured and simulated absorptance spectra are observed to have a same trend and a qualitative fit. Our fabricated plasmonic sensor shows an average sensitivity of 340.0 nm/RIU when applied to a refractive index sensor ranging from 1.0 to 1.6. The proposed substrates provide a practical plasmonic nanorod-based sensing platform, and the fabrication methods used are technically effective and low-cost.