We investigate characteristics of graded-index plastic optical fiber (GI POF) based on a partially fluorinated acrylic polymer. This suggests that the GI POF would significantly reduce reflection noise. By evaluating the angle dependence of scattering intensity for the polymer bulk, we show that the polymer has intrinsically directional forward scattering because of the microscopic heterogeneities. The noise reduction is closely related to the intrinsic scattering because of the microscopic heterogeneities. The low-noise GI POF improves transmission quality in spite of the partial detection with photodetector that increases loss and noise. The GI POF based on the partially fluorinated acrylic polymer could be candidate for multilevel transmission with higher signal-To-noise ratio.