The experimental results presented here show that the use of luminescent multimode fibers in sensors of the refractive index of the ambient medium makes it possible to substantially increase their sensitivity to variation of the medium's refractive index. Experiments have been carried out with fibers made from silicate glass containing luminescent centers in the form of neutral molecular clusters of silver. The sensitivity is increased because more high-order modes are excited when the fiber captures the radiation of luminescent centers in the fiber than when the waveguide modes are excited through the ends of the fiber. The results of numerical modelling show that the sensitivity is appreciably increased for modes with index N ≥ 100.