The refractive index sensing properties of a period array of subwavelength metallic slits in water environment are investigated. The transmission spectra of the slit array are calculated with a rigorous fully-vectorial method. A simple semi-analytical Fabry-Perot model that can accurately reproduce the rigorous fully-vectorial data is built up. We find that the transmission peak becomes sharpest as it is exactly located at the Rayleigh anomaly position, which is explained based on the resonance condition derived from the model. The method to design the slit array to achieve this sharpest transmission peak is presented. The full width at half-maximum (δλ) of the designed transmission peak can be as low as 0.01 nm, which corresponds to a refractive-index measurement uncertainty (δns) of 2× 10-6 RIU. The influences of array period, slit width and incident angle on the designed sensitivity, δλ, δns and peak transmittance of the sensor are systematically provided.