A polymer waveguide with 4-channel graded-index circular cores is fabricated by the preform method. Very low loss (0.028 dB/cm at a wavelength of 850 nm) and high bandwidth (83 Gbps for 1 m, estimated) properties are experimentally demonstrated by the new waveguide for the first time. By densely aligning the cores during the preform fabrication, a waveguide with a pitch size of 56 mum and a core diameter of 50 mum is obtained, which is expected to be utilized in high-speed and high-density parallel optical interconnections.