An optimum index profile offering the highest bit rate communication was formed in a poly methyl methacrylate (PMMA)-based graded-index plastic optical fiber (GI-POF) by modifying the polymerization process. The interfacial-gel polymerization process we have proposed to fabricate the PMMA-based GI-POF is capable of forming a nearly optimum refractive index profile. However, the theoretically calculated bandwidth from the measured index profile was reduced compared with a GI-POF with an optimum profile. In this paper, we report how to obtain a PMMA-based GI-POF having exactly the optimum index profile. The bandwidth of this ideal GI-POF was experimentally measured and a very high value of 2.88 GHz, even for a 150-m fiber length, was confirmed. The calculated bandwidth agreed well with the experimentally measured one. These results indicate that very low modal dispersion can be expected in a GI-POF fabricated by the modified interfacial-gel polymerization process.