In this paper, we propose a low loss and cost-effective assembly in optical transceiver for on-board applications by applying graded-index (GI) core polymer waveguides to effectively couple the signal light between light sources/photodetectors and multimode fibers (MMFs). In order to satisfy the requirements for higher bandwidth data transmission, on-board optical interconnects have been anticipated in datacenter networks. When applying active optical cables (AOCs) to the on-board interconnects, the assembly density between optical devices and fibers is an important issue. Hence, polymer optical waveguides with densely aligned cores are one of the promising candidates to be an interface between the active components and fibers. In this paper, GI circular core polymer optical waveguides are applied to the onboard wiring. We demonstrate the ability of GI core waveguide to achieve low-loss coupling with optical transceivers due to tightly confined optical field in the core. Furthermore, we propose to utilize the lens function of GI core in the transceiver assembly. We theoretically demonstrate that the GI core enables to improve the coupling efficiency by 0.6 dB as a cylindrical lens. Meanwhile, by just inserting a perpendicularly bent GI core waveguide between an optical transmitter and an MMF, we successfully transmit a 53.125-Gbit/s PAM4 optical signals experimentally.