Plasmonic nanostructures with large local field enhancement have been extensively investigated for sensing applications. However, the quality factor and thus the sensing figure of merit are limited due to relatively high ohmic loss. Here we propose a novel plasmonic sensor with ultrahigh figure of merit based on super-narrow Rayleigh anomaly (RA) in a mirror-backed dielectric metasurface. Simulation results show that the RA in such a metasurface can have a super-high quality factor of 16000 in the visible regime, which is an order of magnitude larger than the highest value of reported plasmonic nanostructures. We attribute this striking performance to the enhanced electric fields far away from the metal film. The super-high quality factor and the greatly enhanced field confined to the superstrate region make the mirror-backed dielectric metasurface an ideal platform for sensing. We show that the figure of merit of this RA-based metasurface sensor can be as high as 15930/RIU. Additionally, we reveal that RA-based plasmonic sensors share some typical characteristics, providing guidance for the structure design. We expect this work advance the development of high-performance plasmonic metasurface sensors.