Plasmonic sensor based on metallic nanostructures is a promising platform for applications, such as biology, chemistry, materialogy, photonics and bioscience due to their attractive properties. However, the sensitivity of plasmonic sensors is usually limited by broad-spectral features due to large radiative loss of metallic nanostructures in visible region. in this paper, we introduce structural asymmetry to generate the Fano resonance in the metallic nanostructure composed of asymmetric ellipsoidal pair. The distinct Fano-like resonance around wavelength of 681 nm possesses sharp peak as narrow as 10.8 nm. And the Fano mode exhibits high refractive index sensitivity as large as 299 nm/RiU. Due to the excitation of sharp spectral features, high figure of merit of 27.8 at the Fano resonance is obtained in a wide refractive index range of 1.0~1.1. This device is promising for the applications of high sensitivity microchip sensor.