A multipoint fiber optic refractometer that uses an algorithm to compensate for the nonlinearity generated by an optical frequency sweeping laser is presented. This compensation allows for designing the multipoint sensing system. Otherwise, only single-point sensing is possible. Also, the nonlinearity compensation, applied to all sensing points simultaneously, permits an improvement in the resolution of each sensing point after the compensation is performed. The mathematical model and experimental results of the proposed multipoint refractive index sensor are presented.