A novel, to our knowledge, device based on a tapered optical fiber with a double-layer deposition including a metallic media is presented, and its properties are studied. The main novelty of the device consists of the introduction of a dielectric layer, whereas the systems depicted in the literature are simply metal-coated tapered fibers. The presence of the dielectric layer permits one to tune the response of the device to the refractive index of the surrounding medium. We have proved the suitability of this scheme for refractive-index sensing by depicting two measurement modes, namely, total power attenuation and spectral transmittance.