In this paper, we represent low-loss Y-branched multimode polymer optical waveguides with graded-index (GI) cores applicable to an optical coupler as a MUX device in coarse wavelength division multiplexing links. We apply the Mosquito method as well as the imprint method to form the Y-branched structures in polymers. We experimentally confirm that the insertion loss (including the coupling, propagation, bending, and multiplexing losses) in the multimode GI-core Y-branched waveguide is approximately 1-dB lower than the same Y-branched waveguide with step-index (SI) core. In addition, we also succeeded in fabricating Y-branched single-mode polymer waveguides applying the Mosquito method. In order to satisfy the single-mode condition, the core diameter needs to decrease to 10 mm and less.