In this paper, a refractive index sensor based on the control of the fiber core refractive index is proposed. By employing ultraviolet curable adhesive with the different refractive index and hollow capillary fiber, the special fiber with a variable core refractive index is fabricated. Using the special fiber, a novel, to the best of our knowledge, refractive index surface plasmon resonance (SPR) sensor with a controllable detecting range of refractive index is realized. Functional testing of the sensing probes with the core refractive indices of 1.590, 1.516, and 1.454 is performed respectively, indicating that their sensitivities are 1580 nm/RIU, 2220 nm/RIU, and 3467 nm/RIU, respectively, and their detecting ranges of refractive index are 1.385-1.435 RIU, 1.365-1.415 RIU, and 1.335-1.385 RIU, respectively. Furthermore, in order to explore the detection effect of the sensing probe with the higher-core refractive index, we conducted theoretical calculation using the Kretchmann model. The experimental and simulating results indicates that, with the increase of the core refractive index, the magnitude of refractive index that can be detected increases. This study provides a new method for the detection of high refractive index solutions and a new idea for the fabrication of wavelength-division multiplexing distributed SPR sensors.