This Letter presents a plasmonic nanostructure consisting of a nanodisk and a nanoring. The nanodisk is outside of the nanoring. The quadrupolar, hexapolar, and octupolar resonance modes of the nanoring are excited easily by the bright dipolar mode of nanodisks. This nanostructure shows strong interaction and deep Fano dips. In addition, the resonance frequency, depth, and line width of Fano dips can be tuned by changing the geometrical parameters of the nanodisk and nanoring. These plasmonic nanostructures show both high contrast ratio and high figure of merit. Such characters make them suitable for chemical and biological sensing.