Sub-wavelength metal-dielectric-metal (MDM) composites support localized elec- tromagnetic modes that are strongly conflned in periodic structures. These modes can be con- trolled by tuning the shape of the composites as we demonstrated in previous works. Moreover, the Localized Surface Plasmon Resonance (LSPR) can be applied in new sensor applications. In this paper, we use the Finite-Difierence Time-Domain (FDTD) method to study double-periodic metal-dielectric-metal composites and put emphasis to interactions with the dielectric cover layer. The numerical results demonstrate that variation of the refractive index (RI) of the cover layer as well as the layer thickness afiect the LSPR response of the proposed MDM composite. The resonance-curve min/max groove period, the resonance-curve width, and the resonance-curve amplitudes from the MDM sensor output indicate that the proposed composite may flnd use as an efiective sub-wavelength dielectric sensing optical component for photonic applications.