Localized surface plasmon resonance (LSPR) based sensors exhibit enormous potential in the areas of medical diagnosis, food safety regulation and environmental monitoring. While, the broadband spectral lineshape of LSPR hampers the observation of wavelength shifts in sensing processes, thus preventing their widespread applications in sensors. Here, we describe an improved plasmonic sensor based on Fano resonances between LSPR and Rayleigh anomaly (RA) in a metal-insulator-metal (MIM) meta-grating, which is constructed by silver nanoshells array, an isolation grating mask and a continuous gold film. The MIM configuration offers more freedoms to control the optical properties of LSPR, RA and the Fano resonance between them. Strong couplings between LSPR and RA form a series of narrowband reflection peaks (with a linewidth of ~20 nm in full width at half maximum (FWHM) and a reflectivity closing to 100%) within a LSPR based broadband extinction window in experiment, making the meta-grating promising for applications of high-efficiency reflective filters. While, a well-optimized Fano resonance between LSPR and RA by carefully adjusting the angles of incident light can switch such nano-device to an improved biological/chemical sensor with the figure of merit (FOM) large than 60 and capability for detecting the local refractive index changes caused by the bonding of target molecules on surface of the nano-devices. The figure of merit of hybrid sensor in detection of target molecules is 6 and 15 times higher than the simple RA and LSPR based sensors, respectively.