An optical fiber refractive index (RI) sensor based on a single-mode–multimode–single mode (SMS) fiber structure fabricated with a coreless low-index multimode fiber (CLIMF) tapered to several diameters is presented. Both the response to changes in the external RI and its spectral dependence were strongly influenced by the length and diameter of the CLIMF. Different SMS sensors with diameters of 120, 100, 80, 60, 40  μm and the corresponding reimaging lengths at 1550 nm are immersed in RI of 1.32, 1.34, 1.36, 1.39, and 1.42 to study the response to changes in the external RI. The diameter of 80  μm yields the best sensitivity (540.7  nm  /  RIU) with a resolution of 6  ×  10^−  5 in the RI range 1.32 to 1.39. By duplicating the reimaging length at 1550 nm for this diameter, the RI range increased to 1.42 and a maximum sensitivity of 1022  nm  /  RIU is achieved in the RI range from 1.39 to 1.42. Also the simulation results corroborate the wavelength positions of the peaks of the experimental spectrums. We show that the response range to changes in the external RI is controlled with the SMS geometry. This advantage makes the SMS sensor very suitable for biological applications.