We present polymer optical waveguides with graded index (GI) circular core that have unique structures on their ends to enable very low-loss 90-degree vertical optical path conversion. In general, the signal light from the VCSELs mounted on optical printed circuit boards (OPCBs) needs to be perpendicularly bent in order to couple to the waveguides integrated on board and similarly from the waveguide to the photodetectors. Therefore, optical path conversion structures between horizontal and vertical directions are required on the ends of waveguides. In the case of multimode polymer optical waveguides with step-index (SI) core, 45-degree mirrors at the waveguide ends should be a well-known technique when they are integrated on boards. However, a couple of dB of optical loss at lowest has generally been observed at the mirrors, which is very critical for the limited link power budget of polymer waveguide links. In this paper, we demonstrate that GI-cores in polymer waveguides enable 3-dB loss advantage over the SI-core waveguides in the optical path conversion.