In this paper, the coupled Ag-shell/dielectric-core nanorod for sensor application is investigated and the different dielectric core plasmonic metamaterial is adopted in our design. The operational principle is based on the concept of combining the lattice resonance, localized surface plasmon resonance (SPR), and cavity plasmon resonance modes within the nanostructure. The underlying mechanisms are investigated numerically by using the three-dimensional finite element method and the numerical results of coupled solid Ag nanorods are included for comparison. The characteristic absorptance/reflectance peaks/dips have been demonstrated to be induced by different plasmonic modes that could lead to different responses required for plasmonic sensors. A nearly perfect absorptance and an approximate zero reflectance with a sharp band linewidth are obtained from the proposed system, when operated as an SPR sensor with the sensitivity and figure of merit of 757.58 nm/RIU (RIU is the refractive index unit) and 50.51 (RIU-1), respectively. Our work provides a promising method for the future developments of more advanced metamaterial absorber for chemical sensing, thermal radiation tailoring, field enhanced spectroscopy, and general filtering applications.