We demonstrate that graded-index (GI) core polymer optical waveguides are a promising component realizing highbandwidth- density on-board interconnects. As a method for fabricating GI-circular-core polymer optical waveguides, we introduce the Mosquito method utilizing a microdispenser. The Mosquito method is capable of accurately controlling the core diameter and the inter-core pitch. We also demonstrate that the GI-core polymer waveguides enable remarkably low loss waveguide circuits involving waveguide crossings in a mono layer. We show an alternative technique to realize the low-loss GI-core crossed waveguide: the photo-addressing method which was developed by Sumitomo Bakelite Co., Ltd.