We successfully fabricate a polymer optical waveguide with multiple graded-index (GI) cores directly on a substrate utilizing the soft-lithography method. A UV-curable polymer (TPIR-202) supplied from Tokyo Ohka Kogyo Co., Ltd. is used, and the GI cores are formed during the curing process of the core region, which is similar to the preform process we previously reported. We experimentally confirm that near parabolic refractive index profiles are formed in the parallel cores (more than 50 channels) with 40 microm x 40 microm size at 250-microm pitch. Although the loss is still as high as 0.1 approximately 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 step-index (SI)-core waveguides with the same materials by means of the same process. Then, we evaluate the inter-channel crosstalk in the 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 inter-channel crosstalk allows the GI-core waveguides to be utilized for extra high-density on-board optical interconnections.