Introducing a conducting metal layer and the structural asymmetry to elliptical annular aperture arrays, multiple plasmonic coupled-resonant modes are generated under normal incidence in the visible light range. The electromagnetic fields can be strongly enhanced at resonant modes in this device, which increases the interaction volume of the detected analyte and optical fields; therefore, multiple plamonic coupled modes exhibit higher refractive index sensitivity than as large as 610 nm/RIU. The distinct Fano-like resonance around a wavelength of 681 nm originates from the interference between bonding dipolar and the quadrupolar modes. Due to the excitation of sharp spectral features as narrow as 7 nm, high figure of merits of 94 at the Fano-like dip is obtained in a wide refractive index range of 1.33-1.40. Furthermore, to generate strong Fano-like resonance, the geometric shape of ellipse is selected, which is a good geometric shape candidate compared to the circle shape. This device is promising for biosensing applications with high sensitivity and low limit of detection.