In this paper, we propose a higher efficiency optical coupling technique using 90-degree-bent Graded-Index (GI) core polymer waveguide which replaces conventional optical assembly (mirrors and lenses) in vertical cavity surface emitting laser (VCSEL) based optical engines. The 90-degree-bent GI-core polymer waveguides are fabricated using the Mosquito method. However, high coupling loss could be caused by the VCSEL beam divergence due to diffraction in the lens free coupling. We theoretically confirm that total insertion loss including bending loss as well as coupling loss could remain low by the waveguide NA control. Fabricating the 90-degree-bent GI-core polymer waveguides with the optimized NA, a waveguide insertion loss as low as about 2 dB is experimentally achieved.