We have investigated, in a numerical and experimental way, a refractive index (RI) sensor based on surface plasmon resonance (SPR) in a silver-coated light-diffusing fiber (LDF). The experimental tests were conducted using water-glycerine mixtures with refractive indices ranging from 1.332 to 1.388. In the considered refractive index range, the experimental results show a sensitivity of the SPR wavelength to the outer medium’s RI ranging from ~2600 to ~4700 nm/RIU, which is larger than the sensitivity recently reported for a gold-coated LDF sensor (~1200 to ~4000 nm/RIU). The silver-coated sensor is also shown to ensure a higher signal-to-noise ratio (SNR) compared to the gold-coated sensor.