We succeeded in utilizing the soft-lithography method for fabricating a polymer waveguide with GI cores directly on a substrate. A UV-curable polymer (TPIR-202) supplied from Tokyo Ohka Kogyo Co. Ltd. is used to form the matrix of polymer waveguide. The GI cores are formed during the curing process of the core region, which is similar to the preform process we have reported. We experimentally confirm that near parabolic refractive index profiles were formed in the parallel cores (8 to 16 channels) with 80 um x 80 um size at 250-μm pitch. Although the loss is still as high as 0.2 - 0.3 dB/cm at 850 nm, which is mainly due to scattering loss inherent to the polymer matrix, the scattering loss attributed to the waveguide's structural irregularity could be sufficiently reduced by a graded refractive index profile. For comparison, we fabricate SI-core waveguides with the same materials by means of the same process. Then, we evaluate the inter-channel crosstalk in SI- and GI-core waveguides under almost the same conditions. It is noteworthy that remarkable crosstalk reduction (5 dB and beyond) is confirmed in the GI-core waveguides, since the propagating modes in GI-cores are tightly confined near the core center and less optical power is found near the core cladding boundary. This significant improvement in the interchannel crosstalk allows the GI-core waveguides to be utilized for extra high-density on-board optical interconnections.