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Polystyrene (PS) was selected as a costless polymer matrix for graded index polymer optical fibers (GI POFs) with low attenuation at a wavelength of 670 nm. However, fabricated PS-based GI POFs showed attenuation of more than 300 dB/km. This high attenuation PS-based GI POF had a quite broad molecular weight distribution. In contrast, a PS-based GI POF with a narrow molecular weight distribution showed low attenuation of around 160 dB/km. This is because the refractive index of PS, different from general polymers, is greatly affected by the molecular weight. The PS-based GI POF showed the high thermal stability of this low loss performance at a temperature of 70°C , despite the low glass transition temperature caused by plasticization. The measured refractive index profile was near optimum (g=2.5), and a high bandwidth of 5.8 GHz for a 50 m length was obtained.