The behavior of tapered graded-index polymer optical fibers is analyzed computationally for different refractive indices of the surrounding medium. This serves to clarify the main parameters affecting their possible performance as refractive-index sensors and extends an existing study of similar structures in glass fibers. The ray-tracing method is employed, its specific implementation is explained, and its results are compared with experimental ones, both from our laboratory and from the literature. The results show that the current commercial graded-index polymer optical fibers can be used to measure a large range of refractive indices with several advantages over glass fibers.