Using the Mosquito method, we fabricate low-loss multimode polymer optical waveguides with graded-index (GI) perfect circular cores for the applications to on-board optical interconnection. We already developed the Mosquito method utilizing a microdispenser, as a fabrication technique for GI circular core polymer waveguides. In the Mosquito method, a liquid-state core monomer is dispensed from a syringe needle into a liquid-state cladding monomer while the needle horizontally scans. Originally we used siloxane based monomers. In this paper, novel organic-inorganic hybrid materials (SUNCONNECT®) are selected to confirm the applicability of wide-range polymers to the Mosquito method. Here, a dip is observed on the upper perimeter of the obtained core cross-sections particularly when using a straight needle. Such a core-shape deformation increases the coupling loss with circular-core optical fibers. So, the flow of core and cladding monomers while dispensing the core with the needle scan is visually observed. It is confirmed that the edge of the straight needle chips off the upper perimeter of the core when the core monomer is dispensed, leading to the dip. Therefore, the straight needle is replaced for a curved one to change the dispensing direction for eliminating the dip. It is experimentally found that an almost circular core (50-μm diameter with 1.09 vertical to horizontal ratio of diameter) is formed when a curved needle is used. Finally, we successfully demonstrate a 1.73-dB lower loss in a 5-cm long waveguide compared to the one having the core with a dip.