Plasmonic gap mode in metal-insulator-metal (MIM) structure has proven promising for refractive index sensing due to its near unity absorption. However, the sensing performance of gap mode has been limited by the broad resonance band, which is related to high plasmonic loss. In this work, square-patch-based MIM structures are used for simultaneous excitation of both the surface plasmon polariton and Rayleigh anomaly with large absorptions, and demonstrate their excellent sensing performances. For the Rayleigh anomaly, the sensitivity and full width half-maximum are 1470 nm/RIU and 0.23 nm, respectively. The corresponding figure of merit is calculated to be 6400 in wavelength shift form and 58,800 in intensity variation form. It is also observed that the two Wood's anomalies have reverse incident-angle-dependent properties, which can be explained by the opposite propagating direction of surface waves.